alex.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import planarity as pl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from collections import deque\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "edges = {\n",
    "    'k3': [(1,2), (1,3), (2,3)],\n",
    "    'k5': [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)],\n",
    "    'k8': [(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (3, 4),\n",
    "           (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8), (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (7, 8)],\n",
    "    'k9': [(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8),\n",
    "           (2, 9), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (5, 6), (5, 7),\n",
    "           (5, 8), (5, 9), (6, 7), (6, 8), (6, 9), (7, 8), (7, 9), (8, 9)],\n",
    "    'g1': [(1, 2), (1, 10), (1, 16), (1, 19), (1, 20), (1, 21), (1, 25), (1, 30), (1, 31), (2, 10), (2, 17), (2, 19), (2, 20),\n",
    "           (2, 21), (2, 25), (2, 29), (2, 30), (2, 31), (3, 5), (3, 6), (3, 7), (3, 12), (3, 16), (3, 19), (3, 21), (3, 23),\n",
    "           (3, 33), (4, 8), (4, 9), (4, 11), (4, 15), (4, 23), (4, 24), (4, 26), (4, 27), (4, 28), (5, 6), (5, 7), (5, 12),\n",
    "           (5, 16), (5, 19), (5, 21), (5, 23), (5, 33), (6, 7), (6, 12), (6, 16), (6, 21), (6, 23), (6, 25), (6, 31), (6, 33),\n",
    "           (7, 12), (7, 16), (7, 19), (7, 21), (7, 23), (7, 33), (8, 9), (8, 11), (8, 15), (8, 18), (8, 24), (8, 27), (8, 28),\n",
    "           (9, 11), (9, 15), (9, 16), (9, 24), (9, 26), (9, 27), (9, 28), (10, 19), (10, 20), (10, 21), (10, 23), (10, 25),\n",
    "           (10, 30), (10, 31), (11, 15), (11, 18), (11, 24), (11, 27), (11, 28), (12, 16), (12, 19), (12, 20), (12, 23),\n",
    "           (12, 33), (13, 14), (13, 17), (13, 18), (13, 22), (13, 23), (13, 26), (13, 29), (13, 32), (14, 16), (14, 17),\n",
    "           (14, 18), (14, 22), (14, 26), (14, 29), (14, 32), (15, 18), (15, 24), (15, 27), (15, 28), (16, 19), (16, 21),\n",
    "           (16, 22), (16, 32), (16, 33), (17, 18), (17, 22), (17, 26), (17, 29), (17, 32), (18, 22), (18, 24), (18, 27),\n",
    "           (18, 29), (18, 32), (19, 20), (19, 30), (19, 33), (20, 23), (20, 25), (20, 30), (20, 31), (21, 23), (21, 25),\n",
    "           (21, 30), (21, 31), (21, 33), (22, 26), (22, 29), (22, 32), (23, 25), (23, 26), (23, 28), (23, 30), (23, 31),\n",
    "           (23, 33), (24, 27), (24, 28), (25, 30), (25, 31), (26, 28), (26, 29), (26, 32), (27, 28), (29, 32), (30, 31)],\n",
    "    'g2': [(1, 5), (1, 8), (1, 14), (1, 16), (1, 17), (1, 18), (1, 20), (1, 23), (2, 6), (2, 7), (2, 13), (2, 21), (2, 22),\n",
    "           (2, 26), (2, 31), (2, 32), (2, 33), (3, 4), (3, 6), (3, 9), (3, 15), (3, 16), (3, 18), (3, 25), (3, 27),\n",
    "           (3, 30), (4, 6), (4, 9), (4, 15), (4, 18), (4, 20), (4, 25), (4, 27), (4, 30), (5, 8), (5, 14), (5, 16), (5, 17),\n",
    "           (5, 18), (5, 20), (5, 23), (6, 7), (6, 9), (6, 13), (6, 15), (6, 21), (6, 27), (6, 30), (6, 31), (6, 32), (6, 33),\n",
    "           (7, 13), (7, 21), (7, 22), (7, 24), (7, 29), (7, 32), (7, 33), (8, 14), (8, 16), (8, 17), (8, 18), (8, 20),\n",
    "           (8, 23), (9, 15), (9, 16), (9, 18), (9, 25), (9, 27), (9, 30), (10, 11), (10, 12), (10, 19), (10, 21), (10, 24),\n",
    "           (10, 26), (10, 28), (10, 29), (10, 31), (11, 12), (11, 19), (11, 21), (11, 24), (11, 26), (11, 28), (11, 29),\n",
    "           (11, 31), (12, 19), (12, 24), (12, 26), (12, 28), (12, 29), (12, 31), (12, 32), (13, 21), (13, 22), (13, 24),\n",
    "           (13, 31), (13, 32), (13, 33), (14, 15), (14, 16), (14, 17), (14, 20), (14, 22), (14, 23), (14, 24), (15, 16),\n",
    "           (15, 25), (15, 27), (15, 30), (16, 17), (16, 22), (16, 23), (16, 24), (16, 25), (16, 27), (17, 18), (17, 20),\n",
    "           (17, 23), (18, 20), (18, 23), (18, 25), (18, 27), (18, 30), (19, 24), (19, 26), (19, 28), (19, 29), (19, 31),\n",
    "           (19, 32), (20, 23), (20, 30), (21, 22), (21, 26), (21, 28), (21, 29), (21, 33), (22, 24), (22, 25), (22, 31),\n",
    "           (22, 32), (22, 33), (24, 25), (24, 28), (24, 29), (24, 31), (24, 32), (24, 33), (25, 27), (25, 30), (26, 28),\n",
    "           (26, 29), (26, 31), (27, 30), (28, 29), (28, 31), (29, 33), (31, 32), (32, 33)],\n",
    "    'g3': [(1, 3), (1, 4), (1, 5), (1, 8), (1, 14), (1, 18), (1, 21), (1, 22), (1, 24), (2, 3), (2, 6), (2, 7), (2, 9), (2, 11),\n",
    "           (2, 13), (2, 16), (2, 21), (2, 24), (3, 4), (3, 5), (3, 6), (3, 8), (3, 9), (3, 11), (3, 12), (3, 14), (3, 15),\n",
    "           (3, 18), (3, 19), (3, 21), (3, 23), (3, 24), (3, 25), (4, 5), (4, 8), (4, 11), (4, 13), (4, 14), (4, 16), (4, 18),\n",
    "           (4, 22), (5, 8), (5, 14), (5, 16), (5, 18), (5, 21), (5, 22), (6, 7), (6, 9), (6, 11), (6, 13), (6, 16), (6, 21),\n",
    "           (6, 24), (7, 9), (7, 11), (7, 13), (7, 16), (7, 21), (7, 22), (7, 24), (8, 14), (8, 16), (8, 18), (8, 21), (8, 22),\n",
    "           (9, 11), (9, 13), (9, 16), (9, 21), (9, 24), (10, 12), (10, 13), (10, 15), (10, 17), (10, 19), (10, 20), (10, 23),\n",
    "           (10, 25), (11, 13), (11, 16), (11, 24), (12, 15), (12, 17), (12, 19), (12, 20), (12, 23), (12, 25), (13, 16),\n",
    "           (13, 17), (13, 20), (13, 24), (14, 16), (14, 18), (14, 21), (14, 22), (15, 17), (15, 19), (15, 20), (15, 23),\n",
    "           (15, 25), (16, 22), (17, 19), (17, 20), (17, 23), (17, 25), (18, 21), (18, 22), (18, 24), (19, 20), (19, 23),\n",
    "           (19, 25), (20, 23), (20, 25), (21, 22), (21, 24), (23, 25)],\n",
    "    'g4': [(1, 2), (1, 4), (1, 5), (1, 6), (1, 10), (1, 16), (1, 23), (1, 24), (1, 25), (2, 7), (2, 8), (2, 9), (2, 10),\n",
    "           (2, 12), (2, 13), (2, 18), (2, 19), (2, 24), (3, 11), (3, 15), (3, 17), (3, 18), (3, 20), (3, 21), (3, 22),\n",
    "           (3, 25), (4, 5), (4, 6), (4, 10), (4, 14), (4, 16), (4, 23), (4, 24), (4, 25), (5, 6), (5, 10), (5, 14), (5, 16),\n",
    "           (5, 18), (5, 23), (5, 24), (6, 9), (6, 10), (6, 14), (6, 16), (6, 18), (6, 19), (6, 23), (7, 8), (7, 9), (7, 12),\n",
    "           (7, 13), (7, 14), (7, 19), (7, 24), (7, 25), (8, 9), (8, 12), (8, 13), (8, 14), (8, 19), (8, 24), (8, 25), (9, 12),\n",
    "           (9, 13), (9, 14), (9, 19), (9, 25), (10, 16), (10, 18), (10, 23), (10, 24), (11, 15), (11, 17), (11, 18), (11, 20),\n",
    "           (11, 21), (11, 22), (11, 25), (12, 13), (12, 14), (12, 19), (12, 24), (12, 25), (13, 14), (13, 16), (13, 19),\n",
    "           (13, 24), (14, 16), (14, 19), (14, 23), (14, 25), (15, 17), (15, 18), (15, 20), (15, 21), (15, 22), (15, 25),\n",
    "           (16, 23), (16, 24), (17, 18), (17, 20), (17, 21), (17, 22), (17, 25), (18, 19), (18, 20), (18, 21), (18, 22),\n",
    "           (20, 21), (20, 22), (20, 25), (21, 22), (21, 25), (22, 25), (23, 24), (23, 25)],\n",
    "    'mg1': [(1, 13), (1, 14), (1, 15), (2, 13), (2, 14), (2, 15), (3, 13), (3, 14), (3, 15), (1, 2), (1, 3), (2, 3), (4, 5),\n",
    "            (4, 6), (5, 6), (7, 8), (7, 9), (8, 9), (10, 11), (10, 12), (11, 12), (13, 14), (13, 15), (14, 15), (1, 4),\n",
    "            (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 7), (4, 8), (4, 9), (5, 7), (5, 8), (5, 9),\n",
    "            (6, 7), (6, 8), (6, 9), (7, 10), (7, 11), (7, 12), (8, 10), (8, 11), (8, 12), (9, 10), (9, 11), (9, 12), (10, 13),\n",
    "            (10, 14), (10, 15), (11, 13), (11, 14), (11, 15), (12, 13), (12, 14), (12, 15)],\n",
    "    'mg2': [(1, 17), (1, 18), (1, 19), (2, 17), (2, 18), (2, 19), (3, 17), (3, 18), (3, 19), (4, 17), (4, 18), (4, 19),\n",
    "            (17, 18), (17, 19), (18, 19), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (5, 6), (5, 7), (5, 8), (6, 7),\n",
    "            (6, 8), (7, 8), (9, 10), (9, 11), (9, 12), (10, 11), (10, 12), (11, 12), (13, 14), (13, 15), (13, 16), (14, 15),\n",
    "            (14, 16), (15, 16), (13, 17), (13, 18), (13, 19), (14, 17), (14, 18), (14, 19), (15, 17), (15, 18), (15, 19),\n",
    "            (16, 17), (16, 18), (16, 19), (1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6),\n",
    "            (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8), (5, 9), (5, 10), (5, 11), (5, 12), (6, 9), (6, 10), (6, 11),\n",
    "            (6, 12), (7, 9), (7, 10), (7, 11), (7, 12), (8, 9), (8, 10), (8, 11), (8, 12), (9, 13), (9, 14), (9, 15), (9, 16),\n",
    "            (10, 13), (10, 14), (10, 15), (10, 16), (11, 13), (11, 14), (11, 15), (11, 16), (12, 13), (12, 14), (12, 15),\n",
    "            (12, 16)],\n",
    "    'mg3': [(1, 25), (1, 26), (1, 27), (1, 28), (2, 25), (2, 26), (2, 27), (2, 28), (3, 25), (3, 26), (3, 27), (3, 28),\n",
    "            (4, 25), (4, 26), (4, 27), (4, 28), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (5, 6), (5, 7), (5, 8),\n",
    "            (6, 7), (6, 8), (7, 8), (9, 10), (9, 11), (9, 12), (10, 11), (10, 12), (11, 12), (13, 14), (13, 15), (13, 16),\n",
    "            (14, 15), (14, 16), (15, 16), (17, 18), (17, 19), (17, 20), (18, 19), (18, 20), (19, 20), (21, 22), (21, 23),\n",
    "            (21, 24), (22, 23), (22, 24), (23, 24), (25, 26), (25, 27), (25, 28), (26, 27), (26, 28), (27, 28), (1, 5), (1, 6),\n",
    "            (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8),\n",
    "            (5, 9), (5, 10), (5, 11), (5, 12), (6, 9), (6, 10), (6, 11), (6, 12), (7, 9), (7, 10), (7, 11), (7, 12),\n",
    "            (8, 9), (8, 10), (8, 11), (8, 12), (9, 13), (9, 14), (9, 15), (9, 16), (10, 13), (10, 14), (10, 15), (10, 16),\n",
    "            (11, 13), (11, 14), (11, 15), (11, 16), (12, 13), (12, 14), (12, 15), (12, 16), (13, 17), (13, 18), (13, 19),\n",
    "            (13, 20), (14, 17), (14, 18), (14, 19), (14, 20), (15, 17), (15, 18), (15, 19), (15, 20), (16, 17), (16, 18),\n",
    "            (16, 19), (16, 20), (17, 21), (17, 22), (17, 23), (17, 24), (18, 21), (18, 22), (18, 23), (18, 24), (19, 21),\n",
    "            (19, 22), (19, 23), (19, 24), (20, 21), (20, 22), (20, 23), (20, 24), (21, 25), (21, 26), (21, 27), (21, 28),\n",
    "            (22, 25), (22, 26), (22, 27), (22, 28), (23, 25), (23, 26), (23, 27), (23, 28), (24, 25), (24, 26), (24, 27),\n",
    "            (24, 28)],\n",
    "#     'mg4': [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), \n",
    "\n",
    "# (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (7, 8), \n",
    "\n",
    "# (9, 10), (9, 11), (9, 12), (10, 11), (10, 12), (11, 12), \n",
    "\n",
    "# (13, 14), (13, 15), (13, 16), (14, 15), (14, 16), (15, 16), \n",
    "\n",
    "# (17, 18), (17, 19), (17, 20), (18, 19), (18, 20), (19, 20), \n",
    "\n",
    "# (21, 22), (21, 23),(21, 24), (22, 23), (22, 24), (23, 24), \n",
    "\n",
    "# (25, 26), (25, 27), (25, 28), (26, 27), (26, 28), (27, 28), \n",
    "\n",
    "\n",
    "# (1, 25), (1, 26), (1, 27), (1, 28), \n",
    "# (2, 25), (2, 26), (2, 27), (2, 28), \n",
    "# (3, 25), (3, 26), (3, 27), (3, 28),\n",
    "# (4, 25), (4, 26), (4, 27), (4, 28), \n",
    "# (1, 5), (1, 6),(1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8),\n",
    "# (5, 9), (5, 10), (5, 11), (5, 12), (6, 9), (6, 10), (6, 11), (6, 12), (7, 9), (7, 10), (7, 11), (7, 12),\n",
    "# (8, 9), (8, 10), (8, 11), (8, 12), (9, 13), (9, 14), (9, 15), (9, 16), (10, 13), (10, 14), (10, 15), (10, 16),\n",
    "# (11, 13), (11, 14), (11, 15), (11, 16), (12, 13), (12, 14), (12, 15), (12, 16), (13, 17), (13, 18), (13, 19),\n",
    "# (13, 20), (14, 17), (14, 18), (14, 19), (14, 20), (15, 17), (15, 18), (15, 19), (15, 20), (16, 17), (16, 18),\n",
    "# (16, 19), (16, 20), (17, 21), (17, 22), (17, 23), (17, 24), (18, 21), (18, 22), (18, 23), (18, 24), (19, 21),\n",
    "# (19, 22), (19, 23), (19, 24), (20, 21), (20, 22), (20, 23), (20, 24), (21, 25), (21, 26), (21, 27), (21, 28),\n",
    "# (22, 25), (22, 26), (22, 27), (22, 28), (23, 25), (23, 26), (23, 27), (23, 28), (24, 25), (24, 26), (24, 27),\n",
    "# (24, 28)]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k3 3\n",
      "k5 10\n",
      "k8 28\n",
      "k9 36\n",
      "g1 154\n",
      "g2 160\n",
      "g3 117\n",
      "g4 117\n",
      "mg1 60\n",
      "mg2 99\n",
      "mg3 154\n"
     ]
    }
   ],
   "source": [
    "for k, es in edges.items():\n",
    "    print(k, len(es))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "graphs = {k: nx.Graph() for k in edges.keys()}\n",
    "for g, es in edges.items():\n",
    "    for e in es:\n",
    "        graphs[g].add_edge(e[0], e[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hYWEh9cs7yypVVVVs374dJ0+exMKFC+Hk5ITMzEyx9PXnn3/i+PHj+Ouvv+Tm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838fcf4a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot()\n",
    "nx.draw(graphs['k5'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kZGTgzp072LFjB6ZNmwZHR0eoq6tDQUEBdnZ2GDNmDNatW4fAwEAkJSUJ1Sj8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\n8adQKJQGyP8BISYkpubQCQwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838d009da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot()\n",
    "nx.draw(graphs['k8'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pl.is_planar(graphs['k5'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pl.is_planar(graphs['k3'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thickness(g):\n",
    "    # Insert into graph until not planar, then move onto next graph\n",
    "    vs = set()\n",
    "    gs = []\n",
    "    current = nx.Graph()\n",
    "    for e in g.edges():\n",
    "        vs.add(e[0])\n",
    "        vs.add(e[1])\n",
    "    \n",
    "    for v in vs:\n",
    "        current.add_node(v)\n",
    "    \n",
    "    for e in g.edges():\n",
    "        current.add_edge(e[0], e[1])\n",
    "        if not pl.is_planar(current):\n",
    "            current.remove_edge(e[0], e[1])\n",
    "            gs.append(current)\n",
    "            current = nx.Graph()\n",
    "            for v in vs:\n",
    "                current.add_node(v)\n",
    "            current.add_edge(e[0], e[1])\n",
    "    gs.append(current)\n",
    "\n",
    "    return gs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thickness2(g):\n",
    "    # Insert by first graph that is still planar after addition\n",
    "    vs = set()\n",
    "    gs = [nx.Graph()]\n",
    "    for e in g.edges():\n",
    "        vs.add(e[0])\n",
    "        vs.add(e[1])\n",
    "    \n",
    "    for v in vs:\n",
    "        gs[0].add_node(v)\n",
    "\n",
    "    for e in g.edges():\n",
    "        added = False\n",
    "        for current in gs:\n",
    "            current.add_edge(e[0], e[1])\n",
    "            if pl.is_planar(current):\n",
    "                added = True\n",
    "                break\n",
    "            else:\n",
    "                current.remove_edge(e[0], e[1])\n",
    "        \n",
    "        if not added:\n",
    "            ng = nx.Graph()\n",
    "            for v in vs:\n",
    "                ng.add_node(v)\n",
    "            ng.add_edge(e[0], e[1])\n",
    "            gs.append(ng)\n",
    "\n",
    "    return gs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thickness3(g):\n",
    "    # Insert by min size graph\n",
    "    vs = set()\n",
    "    gs = [nx.Graph()]\n",
    "    glens = [(0, 0)]\n",
    "    for e in g.edges():\n",
    "        vs.add(e[0])\n",
    "        vs.add(e[1])\n",
    "    \n",
    "    for v in vs:\n",
    "        gs[0].add_node(v)\n",
    "    \n",
    "    for e in g.edges():\n",
    "        added = False\n",
    "        glens.sort()\n",
    "        for gli, (l, i) in enumerate(glens):\n",
    "            current = gs[i]\n",
    "\n",
    "            current.add_edge(e[0], e[1])\n",
    "            if pl.is_planar(current):\n",
    "                added = True\n",
    "                glens[gli] = (l+1, i)\n",
    "                break\n",
    "            else:\n",
    "                current.remove_edge(e[0], e[1])\n",
    "        \n",
    "        if not added:\n",
    "            ng = nx.Graph()\n",
    "            for v in vs:\n",
    "                ng.add_node(v)\n",
    "            ng.add_edge(e[0], e[1])\n",
    "            gs.append(ng)\n",
    "            glens.append((1, len(gs)-1))\n",
    "\n",
    "    return gs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def best_thickness(g):\n",
    "    decomps1 = thickness(g)\n",
    "    decomps2 = thickness2(g)\n",
    "    decomps3 = thickness3(g)\n",
    "\n",
    "    l1 = len(decomps1)\n",
    "    l2 = len(decomps2)\n",
    "    l3 = len(decomps3)\n",
    "    return min(l1, l2, l3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thickness4(g):\n",
    "    # Rotational assignment of edges to one fewer graphs than best known thickness\n",
    "    best = best_thickness(g)\n",
    "    if best == 1:\n",
    "        return thickness2(g)\n",
    "\n",
    "    gs = [nx.Graph() for _ in range(best-1)]\n",
    "    gedges = [e for e in g.edges()]\n",
    "    gedges.sort()\n",
    "    \n",
    "    vs = set()\n",
    "    for e in g.edges():\n",
    "        vs.add(e[0])\n",
    "        vs.add(e[1])\n",
    "    \n",
    "    for v in vs:\n",
    "        for cur in gs:\n",
    "            cur.add_node(v)\n",
    "\n",
    "    not_added = []\n",
    "    for i, edge in enumerate(gedges):\n",
    "        gi = i % len(gs)\n",
    "        gs[gi].add_edge(edge[0], edge[1])\n",
    "        if not pl.is_planar(gs[gi]):\n",
    "            not_added.append(edge)\n",
    "            gs[gi].remove_edge(edge[0], edge[1])\n",
    "    \n",
    "    not_added_again = []\n",
    "    for e in not_added:\n",
    "        added = False\n",
    "        for gcur in gs:\n",
    "            gcur.add_edge(e[0], e[1])\n",
    "            if pl.is_planar(gcur):\n",
    "                added = True\n",
    "                break\n",
    "            else:\n",
    "                gcur.remove_edge(e[0], e[1])\n",
    "                \n",
    "        if not added:\n",
    "            not_added_again.append(e)\n",
    "\n",
    "    if len(not_added_again) > 0:\n",
    "        return thickness2(g)\n",
    "    \n",
    "    return gs\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thickness5(g):\n",
    "    # Like 4 but always assign rather than skipping ahead when an edge makes it non planar\n",
    "    best = best_thickness(g)\n",
    "    if best == 1:\n",
    "        return thickness4(g)\n",
    "\n",
    "    gs = [nx.Graph() for _ in range(best-1)]\n",
    "    gedges = [e for e in g.edges()]\n",
    "    gedges.sort()\n",
    "\n",
    "    vs = set()\n",
    "    for e in g.edges():\n",
    "        vs.add(e[0])\n",
    "        vs.add(e[1])\n",
    "    \n",
    "    for v in vs:\n",
    "        for cur in gs:\n",
    "            cur.add_node(v)\n",
    "\n",
    "    not_added = []\n",
    "    for i, edge in enumerate(gedges):\n",
    "        gi = (i - len(not_added)) % len(gs)\n",
    "        gs[gi].add_edge(edge[0], edge[1])\n",
    "        if not pl.is_planar(gs[gi]):\n",
    "            not_added.append(edge)\n",
    "            gs[gi].remove_edge(edge[0], edge[1])\n",
    "    \n",
    "    not_added_again = []\n",
    "    for e in not_added:\n",
    "        added = False\n",
    "        for gcur in gs:\n",
    "            gcur.add_edge(e[0], e[1])\n",
    "            if pl.is_planar(gcur):\n",
    "                added = True\n",
    "                break\n",
    "            else:\n",
    "                gcur.remove_edge(e[0], e[1])\n",
    "                \n",
    "        if not added:\n",
    "            not_added_again.append(e)\n",
    "\n",
    "    if len(not_added_again) > 0:\n",
    "        return thickness4(g)\n",
    "    \n",
    "    return gs\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thickness6(g):\n",
    "    # Rotational assignment of edges to one fewer graphs than best known thickness\n",
    "    bestg = thickness4(g)\n",
    "    best = len(bestg)\n",
    "    if best == 1:\n",
    "        return bestg\n",
    "\n",
    "    gs = [nx.Graph() for _ in range(best-1)]\n",
    "    gedges = [e for e in g.edges()]\n",
    "    gedges.sort()\n",
    "\n",
    "    vs = set()\n",
    "    for e in g.edges():\n",
    "        vs.add(e[0])\n",
    "        vs.add(e[1])\n",
    "    \n",
    "    for v in vs:\n",
    "        for cur in gs:\n",
    "            cur.add_node(v)\n",
    "\n",
    "    not_added = []\n",
    "    for i, edge in enumerate(gedges):\n",
    "        gi = i % len(gs)\n",
    "        gs[gi].add_edge(edge[0], edge[1])\n",
    "        if not pl.is_planar(gs[gi]):\n",
    "            not_added.append(edge)\n",
    "            gs[gi].remove_edge(edge[0], edge[1])\n",
    "    \n",
    "    not_added_again = []\n",
    "    for e in not_added:\n",
    "        added = False\n",
    "        for gcur in gs:\n",
    "            gcur.add_edge(e[0], e[1])\n",
    "            if pl.is_planar(gcur):\n",
    "                added = True\n",
    "                break\n",
    "            else:\n",
    "                gcur.remove_edge(e[0], e[1])\n",
    "                \n",
    "        if not added:\n",
    "            not_added_again.append(e)\n",
    "\n",
    "    if len(not_added_again) > 0:\n",
    "        return thickness2(g)\n",
    "    \n",
    "    return gs\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compress_decompositions(decomps):\n",
    "    if len(decomps) < 2:\n",
    "        return decomps\n",
    "    new_decomps = [nx.Graph() for _ in range(len(decomps) - 1)]\n",
    "    min_decomp = decomps[-1]\n",
    "\n",
    "    # Add all last graph edges to new first decomp\n",
    "    for e in min_decomp.edges():\n",
    "        new_decomps[0].add_edge(e[0], e[1])\n",
    "    \n",
    "    notAdded = []\n",
    "    for i, decomp in enumerate(decomps[:-1]):\n",
    "        for e in decomp.edges():\n",
    "            new_decomps[i].add_edge(e[0], e[1])\n",
    "            if not pl.is_planar(new_decomps[i]):\n",
    "                new_decomps[i].remove_edge(e[0], e[1])\n",
    "                notAdded.append(e)\n",
    "    \n",
    "    for e in notAdded:\n",
    "        added = False\n",
    "        for g in new_decomps[1:]:\n",
    "            g.add_edge(e[0], e[1])\n",
    "            if not pl.is_planar(g):\n",
    "                g.remove_edge(e[0], e[1])\n",
    "            else:\n",
    "                added = True\n",
    "                break\n",
    "        \n",
    "        if not added:\n",
    "            return decomps\n",
    "    \n",
    "    return new_decomps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_all_vertices(g, vs):\n",
    "    for v in vs:\n",
    "        g.add_node(v)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_edge(g, e):\n",
    "    g.add_edge(*e)\n",
    "    if pl.is_planar(g):\n",
    "        return True\n",
    "    g.remove_edge(e[0], e[1])\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def connect_vertex(g, e):\n",
    "    if nx.has_path(g, e[0], e[1]):\n",
    "        return False\n",
    "    return add_edge(g, e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_tree(g, es):\n",
    "    not_added = []\n",
    "    for e in es:\n",
    "        if not connect_vertex(g, e):\n",
    "            not_added.append(e)\n",
    "    \n",
    "    return not_added"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def connect_length(g, es, l=2):\n",
    "    print (\"Connect length...\")\n",
    "    ges = [e for e in g.edges()]\n",
    "    print(es, ges)\n",
    "    if len(es) == 0:\n",
    "        return []\n",
    "    added = []\n",
    "    max_len = 0\n",
    "    for v, paths in nx.all_pairs_shortest_path(g):\n",
    "        print (paths)\n",
    "        for u, path in paths.items():\n",
    "            if u == v:\n",
    "                continue\n",
    "            target_e = (min(u, v), max(u, v))\n",
    "            print(target_e, es, path, 'Yes' if target_e in es else 'No', len(path), l+1)\n",
    "            max_len = max(max_len, len(path))\n",
    "            if len(path) == l+1 and target_e in es:\n",
    "                if add_edge(g, target_e):\n",
    "                    es.remove(target_e)\n",
    "                    added.append(target_e)\n",
    "    \n",
    "    if len(added) > 0:\n",
    "        # Edges have been added, so lengths have changed, try adding at min length again\n",
    "        not_added = [e for e in es if e not in added]\n",
    "        if len(not_added) == 0:\n",
    "            return []\n",
    "        return connect_length(g, not_added, 2)\n",
    "    elif max_len > l:\n",
    "        # No additions at this length, but longer paths exist\n",
    "        return connect_length(g, es, l+1)\n",
    "    else:\n",
    "        return es\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thickness7(g):\n",
    "    # Create tree before adding any other edges\n",
    "    gs = []\n",
    "    vs = set()\n",
    "    for v in g:\n",
    "        print(v)\n",
    "        vs.add(v)\n",
    "    es = [e for e in g.edges()]\n",
    "\n",
    "    while len(es) > 0:\n",
    "        current = nx.Graph()\n",
    "        add_all_vertices(current, vs)\n",
    "        print(\"es1\", es)\n",
    "        es = make_tree(current, es)\n",
    "        print(\"es2\", es)\n",
    "        es = connect_length(g, es, 2)\n",
    "        print(\"es3\", es)\n",
    "        gs.append(current)\n",
    "    \n",
    "    return gs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k3 1 1 1 1 1 1 1\n",
      "k3 thickness1 1\n",
      "k5 2 2 2 2 2 2 3\n",
      "k5 thickness1 2\n",
      "k8 2 2 2 2 2 2 6\n",
      "k8 thickness1 2\n",
      "k9 3 3 3 3 3 3 7\n",
      "k9 thickness1 3\n",
      "g1 7 3 3 3 3 3 8\n",
      "g1 thickness2 3\n",
      "g2 6 3 4 3 3 3 8\n",
      "g2 thickness2 3\n",
      "g3 7 3 3 3 3 3 7\n",
      "g3 thickness2 3\n",
      "g4 6 3 3 3 3 3 7\n",
      "g4 thickness2 3\n",
      "mg1 4 3 3 3 3 3 7\n",
      "mg1 thickness2 3\n",
      "mg2 6 3 3 3 3 3 9\n",
      "mg2 thickness2 3\n",
      "mg3 11 3 3 3 3 3 10\n",
      "mg3 thickness2 3\n"
     ]
    }
   ],
   "source": [
    "decomps1 = {k: compress_decompositions(thickness(g)) for k, g in graphs.items()}\n",
    "decomps2 = {k: compress_decompositions(thickness2(g)) for k, g in graphs.items()}\n",
    "decomps3 = {k: compress_decompositions(thickness3(g)) for k, g in graphs.items()}\n",
    "decomps4 = {k: compress_decompositions(thickness4(g)) for k, g in graphs.items()}\n",
    "decomps5 = {k: compress_decompositions(thickness5(g)) for k, g in graphs.items()}\n",
    "decomps6 = {k: compress_decompositions(thickness6(g)) for k, g in graphs.items()}\n",
    "decomps7 = {k: compress_decompositions(thickness7(g)) for k, g in graphs.items()}\n",
    "\n",
    "decomps = {}\n",
    "for k in graphs.keys():\n",
    "    l1 = len(decomps1[k])\n",
    "    l2 = len(decomps2[k])\n",
    "    l3 = len(decomps3[k])\n",
    "    l4 = len(decomps4[k])\n",
    "    l5 = len(decomps5[k])\n",
    "    l6 = len(decomps6[k])\n",
    "    l7 = len(decomps7[k])\n",
    "    print(k, l1, l2, l3, l4, l5, l6, l7)\n",
    "    ming = min(l1, l2, l3, l4, l5, l6, l7)\n",
    "    if ming == l1:\n",
    "        print(k, 'thickness1', l1)\n",
    "        decomps[k] = decomps1[k]\n",
    "    elif ming == l2:\n",
    "        print(k, 'thickness2', l2)\n",
    "        decomps[k] = decomps2[k]\n",
    "    elif ming == l3:\n",
    "        print(k, 'thickness3', l3)\n",
    "        decomps[k] = decomps3[k]\n",
    "    elif ming == l4:\n",
    "        print(k, 'thickness4', l4)\n",
    "        decomps[k] = decomps4[k]\n",
    "    elif ming == l5:\n",
    "        print(k, 'thickness5', l5)\n",
    "        decomps[k] = decomps5[k]\n",
    "    elif ming == l6:\n",
    "        print(k, 'thickness6', l6)\n",
    "    elif ming == l7:\n",
    "        print(k, 'thickness7', l7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k3 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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SU1MRFxfHUnAgly9fthgFnTp1CiEhIXU//J966imo1Wq0adNGdFwih8IVQxNV\nVFTA19cXmZmZ6Ny5s+g4bsdoNOLkyZMWo6DaU8J/XgmEhITA09NTdGQih8cVQxN9/fXXUKvVLAU7\nqKioQH5+vsUbyHh7e9cVwNSpU6HVahEQEMBREFEjsRiaqHaMRNZVUlJicUr42LFj6Nq1a90KYMyY\nMdBoNGjXrp3ouEQuhaOkJjh37hzCwsJQVFTELYuNJEkSzp49a/E84MqVK3XvJVz7T3h4OE8JE9kB\ni6EJlixZgl9++QUff/yx6ChOoaqqCkeOHLE4JdyiRQuLXUFdu3blw3wiQVgMjSRJEpRKJf7973+j\nf//+ouM4nBs3blicEjYYDOjUqZPF1dE8JUzkWPiMoZH279+P6upq9OvXT3QUoSRJwoULFyxGQcXF\nxQgPD4dWq0XPnj0xdepUnhImchJcMTTS9OnT4e/vj4ULF4qOYjc1NTU4fvy4xdbQmpqauhVA7f8G\nBQXxlDCRk2IxNEJ5eTl8fX1x+PBh+Pv7i45jE2VlZRZvIJObm4uHH37YYhTk6+vLraFELoS/0jXC\npk2bEBER4TKlcOXKFYtR0MmTJxEcHFxXABMnToRGo+EpYSI3wBVDIwwbNgzx8fGYNGmS6CgNIklS\nvaeEb968aXFKODQ0lKeEidwUi6GBzp49C41Gg+LiYnh5eYmOc1uVlZX1nhJu06aNxSgoMDCQoyAi\nqsNR0p1cugSkpgI5OUBpKdCmDY5evoxnR41yqFK4du2axSnho0ePokuXLnUFMHr0aGi1Wp4SJqK7\n4oqhPpmZQGIikJFh+vOtW3UfKpfJ0KJ5c8hHjgQWLAAiI+0WS5IkFBUVmY2CsrOzcfnyZajVarNR\nUFhYmEOVFxE5DxbD/0pOBubNA8rLgTv9XyOTAV5ewNKlgF5v9RjV1dVmp4Rry8DT09NiFNStWzee\nEiYiq2Ex/FltKZSV3fvXKBRNLoebN2/We0rYz8/PrAC0Wi06dOjQ6O9DRHQvWAy1MjOB6OiGlUIt\nhQLYuROIiLjrp9Z3SrioqAhhYWFmoyCVSoX77ruv4VmIiJqIxVDr8ceBTZvuPD66HZkMGDsW+PLL\nun9lNBrrPSVcVVVlcUo4ODiYp4SJyGGwGADT7qOAALOHzA1l9PTEmsRE7Dtxou6U8EMPPWQxCvLz\n8+PWUCJyaPw1FTBtSW2iiqoqeK5di6ApUzBhwgSo1Wq0bdu26dmIiOyMxQCYzik0YbUAAF6ShAlK\nJTB7tpVsdyaZAAABiklEQVRCERGJwT2OgOnwmjWUlFjndYiIBGIxAIC1Lobz9rbO6xARCcRiAAC1\nGmjqewl7eQEqlXXyEBEJxF1JgFV2JaFlS+DMGeChh6yXi4hIAK4YAKB9eyAmxnQeoTFkMmDECJYC\nEbkErhhq2enkMxGRo+OKoVZkpOnOI4WiYV9Xe1cSS4GIXATPMfxZ7UV4DnC7KhGRKBwl1efAAdP7\nMWzebCqA8vI/PublZSqMESNM78fAlQIRuRgWw51cvmy6LiM313R4zdvbtCU1Lo4PmonIZbEYiIjI\nDB8+ExGRGRYDERGZYTEQEZEZFgMREZlhMRARkRkWAxERmWExEBGRGRYDERGZYTEQEZEZFgMREZlh\nMRARkRkWAxERmWExEBGRGRYDERGZYTEQEZEZFgMREZlhMRARkRkWAxERmWExEBGRGRYDERGZYTEQ\nEZEZFgMREZlhMRARkRkWAxERmWExEBGRGRYDERGZYTEQEZEZFgMREZlhMRARkRkWAxERmWExEBGR\nGRYDERGZ+X/O2i0FtBQWBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838af18208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k5 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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/ly1lNAJ5eRYdwvCXyNixY7Fu3TpJN3uxtO3jzP3+qishXBRYCUGkmMJCacax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\nIg1i+BMRaRDDn4hIg/4/DRXfrwOb+eIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838af48978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k8 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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cuBHLly9HVFQUPv/8c5nPA+RP/hs3boSXlxdsymyQQfSbWmr8S1i2bBmuNGsG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838ab85a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k9 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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bNXXj15ng39Qsn+DgYMyaNQuHDh1Cu3btcOuttyInJwc19UpO/OY3v8Hq1auR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838a9be898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g1 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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Xf7tDl8PZuyjdSP3613FhxQr8DkABwLCaw3QaA3V1ODRzJvDii+j98pf1efUL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\nEUcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838aae3198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g2 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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XgaamwitDL6MRTiqSba5S1TD+jDkuz84UFflfSu6ULEPEVq1iL82ezd5sbh6/\nSc4991x2xRVXMAAsnU4HPNjwcf7557Nzzz036GE4QwY5hTCFZ72UlDEM7ux58dk2JGnUMf6MWY/V\nTnfBFYvf3nrrreyuu+4a/3nBggWssbGRAWB9fX0BjixkjHnL22tq2POJhL/esghk2cNw4y0XMohB\nsHHjlJW4kFchA+3TdVTL+DM2KUSSjkadXXhFHgCbNm1iX//618d/vuCCC9jVV1/NALA9e/YEOLKQ\nIIO37BYfwgOW8clj9ZWNG7mAokjDn+/ai0pwsYB6xt9k+3aWjsXCdaOdxGuvvcYuuuii8Z8//elP\ns8bGRhaLxdizzz4b4MhCgCzeshtkNLYyPYxEsWkTV+F0Y5Ct3kciMo0SCUunJX+2z3Q89JBzbXaz\nlFxyFixYgPfeew+ZseY1kUgEmUwGJSUl+KOorlQ60tYGfPObcoqP2UGEnIJobGaweS6iKIJrrwUe\nfNBZXU5Rkb3MMRHVxRbvCTWN/5jSZ6TQxJ0OxiZKySWmoqIC5eXl+PjjjwFMGP9EIjH+O8IGnZ3A\n5ZcDt94KjIzYe6/5AHj9dW/GZhe3arfmHPCCMKbStrYC//Iv1iWhIxFg2TLgnnuA7m7r0ut+VBeP\nIb+2Ty5ElICbpeRBavxYoL6+Hrt378bcuXMRjUaRTqdRVlaGnp6eoIemFiI6wfktPpYPUXPAK6yo\nZ8pYe5OP1lZeJe6lMrBf1cVQ1fiLWhrJUEpegAULFmDPnj244oorxj3/8vJy9Pb2Bj00dRDVAjR7\nxRi04fIxPOCKoEUUReP1Q02U4q8F1DT+Xih9Skp9fT127doFAOOef3V1NQ4ePBjwyBTBqcb8dMiy\nYvQxPEDkwKuHmijFXwuoGfMPo9LnNJiePzAR86+pqcHhw4cDHpkiuGwBOgVZVow+hgcIH3EpZzMu\nPW4BNY1/WJU+c2DG/AHu+WcyGcyaNQv9EnQCkh4BLUBzIsOKUdQcIOTDJ+lxNY2/COElxpRohlJX\nV4fBwUEcOnQIkUgE6XQadXV1OHbsWNBDkx+vtOFlWDGKmgOEfPgkPa6m8R9bGjnM8leqK5NhGOOh\nn2g0CsYY5syZg0Fq3l4YLzoyybJi9DE8QASAD/USahp/AFi3DsNO36tYV6Zs459OpzFv3jyM2M1T\n1xEvNkVlWjFSZ7Jw43G9hHrZPqkUX853deFDAOcDiNp5v4Jdmcy4vxnzP/vss5FOp5HJZBCJqPv8\n9hzRm6Kh5NECAAANr0lEQVSyrRjN8IDdbKag50DWHMaRI/x7WrQIWLNGnmsrC16mlroXvvCJPCJc\nmbGXshotBdi6dStbtWoVu/LKK9lFF13ERkdHGQB28ODBoIcmN6I7MsmqCaWKTlEYhPRChBrG3+LN\nnfMhYN5UyaScE9cCu3fvZmeffTa76qqr2IUXXsgYYywSibBORc/HN0QoJKoiPpanIZAUc0CVB5RG\nyB/2sVGdaW6LZCIRRM4/H1iyRN1S8izOPvtsfPzxx7jgggvGRd6Kioqwb98+LFUofOU75qZoR4e7\nzBYVxMdkllOwU2GdLaQHyH3NFcdgTOJ8r85O3pvSSXVmaSnfBAmJcayvr8ecOXPw5z//GW+//TYq\nKyuxfv16fPvb3w56aHLj5h4CuBBcW1to7iPfoTksLXLvFsooWRsEqRS+G43in/7wB9y/bx/Q3Iyb\nMxkc/uCDoEcmPw5zptMAUF8P1NUBL70kvQKstNAclhZ5Pf9UCpg3z12edjzO5VRVDfl0dvKb/5ln\ncGJ0FMWjo+P/NQoe5orOmQNcfTVw++3qnqcfmKGHwcGCISCGiRAigAm1xhUreHpkQ4OXIw0PNIel\nRl7PX6Rss4q0t/PlckcHMDQ0yfADPEc3CgD79/NGE3V1QDLJHxjEVArlTGcxpaRmcJAbsI4O/p3I\n1tRFVnSfw5Ijr/HXSLZ5CtkbZFYXZqOjZJwKYW6KdncDd94JtLQACxcCUYuVIjJ39ZIRneewAshr\n/DWSbZ6EGwliMk7WMOV4164F9u613w5Utq5esqLrHFYEeY2/RrLNkxAhQUzGyRq0Gektus5hRZDX\n+Gsk2zyOSAliMk75EdED98knKQsoHzrOYYWQ1/hrJNs8jsiNLUWa1AeGiGs9Ogr8wz+4P05Y0XEO\nK4S8xl+UZK1KKWKiJYgpU2J6RF3rJ5+k8Np06DiHFUJe4w/oJ1krWoKYMiWmR9S1TqcpvJYP3eaw\nQsht/H3qaCMNXvRlpUyJ3Ii81hRemx7d5rBCyG38AVsdbTKAGiJc0yFig+xkKFMiNyKvNYXX8uND\nVyrCPvIbf6BgdWa6uBhDAD644AJHHW2kQfTGFmVKTI/Iaz04CLz8srjjhRGPu1IR9pFX22c6siRr\nBz7+GM91dmL+l7+M1c8/j+/ffz+uueaaoEfojmTSvQSxCemi5CeZBB5/XMyxolHggQfIaFlBRtlp\nDVHP+Gcx8sknuH3uXPyvhgbsfeMNfGb5csxcvlztdnBuJYhNDIN7UVu2CBlWKOnsBD77WfsVvtMR\njQIXXQR85Stq34OEFqhp/LPULgeHh5HIPoUwKDDaaX4xHaSFbo2VK3mxl0hKSvjDV+V7kAg9asT8\nszlJ7TJx8rMrDAqM2RtkTqBMCet4cY2Gh9W/B4nQo5bxt6N2qbrImblBlkwCMYvdNilTwj5793p3\nbNXvQSLUqBP20bkd3IEDwF13AR0dSO/fDwau5z+OGepauZKHGVQ9zyBobASeesr7z1H9HiRChzqe\nv84KjDU1wP33A93dWPWZz+DHs2djT0MDXkgk8PLs2Vybvrubb+6ScbGHF4V1uVD9HiRChxrGX4QC\nY0iqMDMzZuCFCy/Ev33+87hh9mzc8alPcW16yixxhheFdblgjO8BPPec959FEBZQw/hTO7hxysrK\nUFNTg48++gglJSXoI/kGd/ipGJnJAFdeSfF/QgrUMP7UDm6c8vJyVFZWYt++fYjH4zh06FDQQ1Ib\nt8qTdhkdpQ1gQgosppEEDLWDG6esrAynnnoquru7UV9fT8ZfBOvWAdu3uy+ss4qZAdTQQHs0qRRf\nkXd18XleUcFDcVQk5zlqGH9qBzdOeXk5otEoBgYGEI1GMTo6isHBQSScyuYS3AhfdRXw85/795nm\nBrCuFdhZhZoAJq/st24F1q/PXSRHDwthqGH8Fy3ik8RN6CckImdlZWVIpVKoq6vDyMgIqqur0dfX\nR8bfDZ2dvCmLn2QnIehmtMx6ncHB3EkcZlZfRwdfkZkFi04eFsS0qBHzp3Zw45SXl+Po0aM444wz\nMDg4OG78CRe4SSN2Q0iSEGzhpFDzW98C/uqvxqv6pziBYajqDwA1jD+1gxunvLwc/f39mDVrFo4f\nP47q6mqK+7vBbRqxG0KShGCZzk5nmlUnTgAjI+Gv6vcZNYw/QO3gxigrK8PRo0cxa9YsHDt2DFVV\nVWT83RC0563Tqs2vFZb5AKDeynlRx/hTOzgAE55/bW0tBgYGyPN3i6hG7k4JQRKCJfxeYVFFdUHU\nMf4AtYPDhOc/c+ZMHD16FFVVVRTzd4OoNGInhCQJwRJ+r7BCVNXvFWoZf0D7dnCm519UVISSkhJE\no1Hy/N3gl7ZPLkKShGCJIFZYOm6o20CNVM+TWbqUp35q2A7O9PxHR0dRWVmJ4eFhDAaRqRIWRKQR\nOyUkSQiWCGKFpcKGeoB1C2oaf5OaGi5qphGm5z8yMoKqqiocPXoUw8PDQQ9LXa67jueI+000Gpok\nBEsEtcKSNSTqtMhNIOqFfTQnHo9jdHQUQ0NDmDFjBg4dOkRhHzf4re1jUl8fmiQES/ilnnoyMm6o\nn9SNMKi6BTL+imEYBsrLy3Hs2DHMnDkTvb29tOHrFjdpxE5ZssTfzwuaIPY2ZNxQl6gbIRl/BSkv\nL8fAwABqamqwf/9+8vzd4jSN2A2Vlf59lgwEscKSbUPdaZGbR3ULZPwVpKysDMePH8eMGTPQ19dH\nxl8EZhqxXysAL3sHy4qfKywZq/ol60ZIxl9BysvLcfz4cRQXF2P+/Pno7+9HOp0Oeljq09oKvPoq\nUFfn/We9+KJ+Oeh+rrBkq+qXsBshGX8FMT3/8qEh3GoY+A/DQHrlSqC5GWhr08+oiGTpUuCRR7z/\nHF1z0O0WahYXA0VF9j5Dxqp+CbsRkvFXkCWjo/jWq69i7Q9+gK/u2YP/mU6j+LnngEcfBe64A5g7\nF0gmeYyRsM9bbwExj7OgVchB9wo7hZq//S1w333qV/VL2I1Q7Tx/HWlvxx2vvIKidDr3kzuXFrps\nE0F2urp4u0Wv0TlLy06h5tKlPGS0YQMPfRjG5Nh5IsHDIitX8lCPTB6/iYTdCMn4q8RYmliJlfh+\ndpoYQA8AO/hVjSpjDrrfWC3UVL2qX8JuhGT8VcFtmhj1i7WOH9WoMuagq4CqVf0SdiOkmL8qSJYm\nFmr8qEaVLQed8BYJuxGS8VcBCdPEQo3XRlnGHHTCWyTsRkjGXwUkTBMLNV5Xo8qWg074g2TdCMn4\nq4CEaWKhx6tqVBlz0Al/kKwbIW34qoCEaWKhx5yoTjbZ83HVVZR55SUB6uNbwvzub76ZO2T5QrmG\nwR0Qj9K1Dcb8aqpJOKa5mRdwuaWlBdi82f1xdMJUYSw0Ua0iaxGS6uTTxzfrALzUx7f70Hn99cDr\nFsj4q0BTEy/ackMiAdx5p5ppckGTb6I6obSUV7hS6EcMVh/QXnjSbh86AdYtkPGXnfZ24Kab3Buc\neBzo7pZj6asq2RP1+eeBnh5nxzEM/kDfskXo8LQkWx/fKqJWX0E+dARAxl9mOjt5Jx+3MWcyNmJJ\npYB589xtwtPD2D1u5ofb1VeQDx1BULaPzLgp7MpGhdTCVIorkjY3A42NciuUUuqtHARV+ChZUxbH\nMEJOensZi8cZ4wtK569EgrGNG4M+m+nZuZOxpiZ+riefbyLBf9fUxP9OFlavdv+9AIy1tAR9Juoi\nYn7E44ylUvY/u6mJMcNw9pmGwVgyKf56OIA8f1kR5RV+6UvSLDOnIEkja9tQ6m3weLX6KrQCDVG1\nPeX5y4qIwi4AOPVU98fwAjsxU9kUSiVUaNQO0YWP+bJ2tm4F1q/nWTtnnOHuM4GJh07AmXdk/GUl\nzN6l6gqlEio0aofI+VEoaye7R0YkArhtmSpJtT2FfWQlzN6l6gqlEio0aoeo+ZFKTTgihUI5jLk3\n/CYSOGVk/GVFhKywrN6l6jFTCRUatUPE/CgpAf7wB7HyHVaRwCkj4y8r5F1OjwxpkpIpNGqHiPt6\nZMSfdp0nI4lTRsZfVsLsXYZBoVQyhUbtECW7HUSNqyROGRl/mSHvcnokiJmitXXiAVDICBmGdBWe\nyuNmfsRi/OU3EjllZPxlhrzL6ZEgZgqAG/IdO7h8Rjw+1RglEvz3TU3878jwi8PN/FiyBDhxwptx\n5UMip4xSPWVHIv1vYcTj4UqTXLqUp34GqNCoLU7nx7Zt/owvG8mcMhJ2UwUJ9L+FkUiQKBohFrvz\nQ1SPjGgUyGSUdMrI+KtGGLzLZJIXzDi59UihlMiH1fnR1sardt2uQK+/HvjkEyWdMjL+hP8EKcVL\nEIB4WW4FnTIy/kQwhEAPnVAczVegZPyJ4FC8ExKhOJqvQCnVkwgOSpMkgkTzVGry/Ak5UDBmSoQE\nTVegZPwJgiDClEptETL+BEEQJhqtQMn4EwRBaAht+BIEQWgIGX+CIAgNIeNPEAShIWT8CYIgNISM\nP0EQhIaQ8ScIgtAQMv4EQRAaQsafIAhCQ8j4EwRBaAgZf4IgCA0h408QBKEhZPwJgiA0hIw/QRCE\nhpDxJwiC0BAy/gRBEBpCxp8gCEJDyPgTBEFoCBl/giAIDSHjTxAEoSFk/AmCIDSEjD9BEISGkPEn\nCILQEDL+BEEQGkLGnyAIQkPI+BMEQWgIGX+CIAgNIeNPEAShIf8f5geCIyBm4AwAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838d0e7eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g3 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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wUL8HwYoeIslgtsV8vUe5VvX64dw+JiLJNMrRvlC/30/Dhg2jJ554Ivb5zOye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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838aa3f470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g4 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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oLi/n19Tq1dyyQdM6nv+6zq/p2bN5OLOK+Qh2kYgQswC5xd+OVO+EodSGDWm9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\nO72FAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838d0840f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mg1 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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hKC0tRc+ePQEA9913HyorK3HgwAF8+umn6Ny5M+666y67fWHL3w84qMlsLa14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\nFn+GYZgg5P8DrEaEE6qbF/kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838a71a8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mg2 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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IeHBMTaFPnz6YNXEiWu7bh5M//oihffsCgYHYnZWFO1lZGHXiRLUGJ0KpFPuI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\nA/l/8MPOtw4ac1IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838cffbd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mg3 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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giAiqJkavklYy+NrI1jrq0B7WuYtQ72MwGo348ssvMW/ePJw5cwZJSUmIjo7G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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838aa87a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k, decomp in decomps.items():\n",
    "    print(k, len(decomp))\n",
    "    subplot = 100 + 10*len(decomp)\n",
    "    for cur in decomp:\n",
    "        subplot += 1\n",
    "        plt.subplot(subplot)\n",
    "\n",
    "        nx.draw(cur)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "testings = {k: nx.Graph() for k in graphs.keys()}\n",
    "\n",
    "for k, decomp in decomps.items():\n",
    "    for cur in decomp:\n",
    "        for edge in cur.edges():\n",
    "            testings[k].add_edge(edge[0], edge[1])\n",
    "\n",
    "for k, res in testings.items():\n",
    "    if not nx.is_isomorphic(res, graphs[k]):\n",
    "        print(k, \"is not isomorphic\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  for k, decomp in decomps.items():\n",
    "#     print(k)\n",
    "#     for cur in decomp:\n",
    "#         print(len(cur.edges))\n",
    "#     print('')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# decomp1 = decomps['mg3'][0]\n",
    "# decomp2 = decomps['mg3'][1]\n",
    "# decomp3 = decomps['mg3'][2]\n",
    "# decomp4 = decomps['mg3'][3]\n",
    "\n",
    "# g1 = nx.Graph()\n",
    "# g2 = nx.Graph()\n",
    "# g3 = nx.Graph()\n",
    "\n",
    "# for e in decomp4.edges():\n",
    "#     g1.add_edge(e[0], e[1])\n",
    "\n",
    "# d1_remainder = []\n",
    "# for e in decomp1.edges():\n",
    "#     g1.add_edge(e[0], e[1])\n",
    "#     if pl.is_planar(g1):\n",
    "#         continue\n",
    "#     else:\n",
    "#         g1.remove_edge(e[0], e[1])\n",
    "#         d1_remainder.append(e)\n",
    "# print(len(d1_remainder))\n",
    "\n",
    "# for e in d1_remainder:\n",
    "#     decomp2.add_edge(e[0], e[1])\n",
    "#     if not pl.is_planar(decomp2):\n",
    "#         decomp2.remove_edge(e[0], e[1])\n",
    "#     else:\n",
    "#         continue\n",
    "#     decomp3.add_edge(e[0], e[1])\n",
    "#     if not pl.is_planar(decomp3):\n",
    "#         decomp3.remove_edge(e[0], e[1])\n",
    "#     else:\n",
    "#         continue\n",
    "        \n",
    "#     print(\"Not working...\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "es1 [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]\n",
      "es2 [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]\n",
      "Connect length...\n",
      "[(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]\n",
      "{1: [1], 2: [1, 2], 3: [1, 3], 4: [1, 4], 5: [1, 5]}\n",
      "(1, 2) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [1, 2] No 2 3\n",
      "(1, 3) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [1, 3] No 2 3\n",
      "(1, 4) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [1, 4] No 2 3\n",
      "(1, 5) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [1, 5] No 2 3\n",
      "{2: [2], 1: [2, 1], 3: [2, 3], 4: [2, 4], 5: [2, 5]}\n",
      "(1, 2) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [2, 1] No 2 3\n",
      "(2, 3) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [2, 3] Yes 2 3\n",
      "(2, 4) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [2, 4] Yes 2 3\n",
      "(2, 5) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [2, 5] Yes 2 3\n",
      "{3: [3], 1: [3, 1], 2: [3, 2], 4: [3, 4], 5: [3, 5]}\n",
      "(1, 3) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [3, 1] No 2 3\n",
      "(2, 3) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [3, 2] Yes 2 3\n",
      "(3, 4) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [3, 4] Yes 2 3\n",
      "(3, 5) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [3, 5] Yes 2 3\n",
      "{4: [4], 1: [4, 1], 2: [4, 2], 3: [4, 3], 5: [4, 5]}\n",
      "(1, 4) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [4, 1] No 2 3\n",
      "(2, 4) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [4, 2] Yes 2 3\n",
      "(3, 4) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [4, 3] Yes 2 3\n",
      "(4, 5) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [4, 5] Yes 2 3\n",
      "{5: [5], 1: [5, 1], 2: [5, 2], 3: [5, 3], 4: [5, 4]}\n",
      "(1, 5) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [5, 1] No 2 3\n",
      "(2, 5) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [5, 2] Yes 2 3\n",
      "(3, 5) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [5, 3] Yes 2 3\n",
      "(4, 5) [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)] [5, 4] Yes 2 3\n",
      "es3 [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]\n",
      "es1 [(2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]\n",
      "es2 [(3, 4), (3, 5), (4, 5)]\n",
      "Connect length...\n",
      "[(3, 4), (3, 5), (4, 5)] [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]\n",
      "{1: [1], 2: [1, 2], 3: [1, 3], 4: [1, 4], 5: [1, 5]}\n",
      "(1, 2) [(3, 4), (3, 5), (4, 5)] [1, 2] No 2 3\n",
      "(1, 3) [(3, 4), (3, 5), (4, 5)] [1, 3] No 2 3\n",
      "(1, 4) [(3, 4), (3, 5), (4, 5)] [1, 4] No 2 3\n",
      "(1, 5) [(3, 4), (3, 5), (4, 5)] [1, 5] No 2 3\n",
      "{2: [2], 1: [2, 1], 3: [2, 3], 4: [2, 4], 5: [2, 5]}\n",
      "(1, 2) [(3, 4), (3, 5), (4, 5)] [2, 1] No 2 3\n",
      "(2, 3) [(3, 4), (3, 5), (4, 5)] [2, 3] No 2 3\n",
      "(2, 4) [(3, 4), (3, 5), (4, 5)] [2, 4] No 2 3\n",
      "(2, 5) [(3, 4), (3, 5), (4, 5)] [2, 5] No 2 3\n",
      "{3: [3], 1: [3, 1], 2: [3, 2], 4: [3, 4], 5: [3, 5]}\n",
      "(1, 3) [(3, 4), (3, 5), (4, 5)] [3, 1] No 2 3\n",
      "(2, 3) [(3, 4), (3, 5), (4, 5)] [3, 2] No 2 3\n",
      "(3, 4) [(3, 4), (3, 5), (4, 5)] [3, 4] Yes 2 3\n",
      "(3, 5) [(3, 4), (3, 5), (4, 5)] [3, 5] Yes 2 3\n",
      "{4: [4], 1: [4, 1], 2: [4, 2], 3: [4, 3], 5: [4, 5]}\n",
      "(1, 4) [(3, 4), (3, 5), (4, 5)] [4, 1] No 2 3\n",
      "(2, 4) [(3, 4), (3, 5), (4, 5)] [4, 2] No 2 3\n",
      "(3, 4) [(3, 4), (3, 5), (4, 5)] [4, 3] Yes 2 3\n",
      "(4, 5) [(3, 4), (3, 5), (4, 5)] [4, 5] Yes 2 3\n",
      "{5: [5], 1: [5, 1], 2: [5, 2], 3: [5, 3], 4: [5, 4]}\n",
      "(1, 5) [(3, 4), (3, 5), (4, 5)] [5, 1] No 2 3\n",
      "(2, 5) [(3, 4), (3, 5), (4, 5)] [5, 2] No 2 3\n",
      "(3, 5) [(3, 4), (3, 5), (4, 5)] [5, 3] Yes 2 3\n",
      "(4, 5) [(3, 4), (3, 5), (4, 5)] [5, 4] Yes 2 3\n",
      "es3 [(3, 4), (3, 5), (4, 5)]\n",
      "es1 [(3, 4), (3, 5), (4, 5)]\n",
      "es2 [(4, 5)]\n",
      "Connect length...\n",
      "[(4, 5)] [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]\n",
      "{1: [1], 2: [1, 2], 3: [1, 3], 4: [1, 4], 5: [1, 5]}\n",
      "(1, 2) [(4, 5)] [1, 2] No 2 3\n",
      "(1, 3) [(4, 5)] [1, 3] No 2 3\n",
      "(1, 4) [(4, 5)] [1, 4] No 2 3\n",
      "(1, 5) [(4, 5)] [1, 5] No 2 3\n",
      "{2: [2], 1: [2, 1], 3: [2, 3], 4: [2, 4], 5: [2, 5]}\n",
      "(1, 2) [(4, 5)] [2, 1] No 2 3\n",
      "(2, 3) [(4, 5)] [2, 3] No 2 3\n",
      "(2, 4) [(4, 5)] [2, 4] No 2 3\n",
      "(2, 5) [(4, 5)] [2, 5] No 2 3\n",
      "{3: [3], 1: [3, 1], 2: [3, 2], 4: [3, 4], 5: [3, 5]}\n",
      "(1, 3) [(4, 5)] [3, 1] No 2 3\n",
      "(2, 3) [(4, 5)] [3, 2] No 2 3\n",
      "(3, 4) [(4, 5)] [3, 4] No 2 3\n",
      "(3, 5) [(4, 5)] [3, 5] No 2 3\n",
      "{4: [4], 1: [4, 1], 2: [4, 2], 3: [4, 3], 5: [4, 5]}\n",
      "(1, 4) [(4, 5)] [4, 1] No 2 3\n",
      "(2, 4) [(4, 5)] [4, 2] No 2 3\n",
      "(3, 4) [(4, 5)] [4, 3] No 2 3\n",
      "(4, 5) [(4, 5)] [4, 5] Yes 2 3\n",
      "{5: [5], 1: [5, 1], 2: [5, 2], 3: [5, 3], 4: [5, 4]}\n",
      "(1, 5) [(4, 5)] [5, 1] No 2 3\n",
      "(2, 5) [(4, 5)] [5, 2] No 2 3\n",
      "(3, 5) [(4, 5)] [5, 3] No 2 3\n",
      "(4, 5) [(4, 5)] [5, 4] Yes 2 3\n",
      "es3 [(4, 5)]\n",
      "es1 [(4, 5)]\n",
      "es2 []\n",
      "Connect length...\n",
      "[] [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]\n",
      "es3 []\n",
      "k5 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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XVFSElStXQiqV4unTp0hLS4Ofnx/XfemdsIRJ59SsWRPbt2/H0KFDYWtri+joaNGRSEPF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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838d0b9eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838a4c3978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f838a894c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8389c45198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "decomp = thickness7(graphs['k5'])\n",
    "print('k5', len(decomp))\n",
    "subplot = 100 + 10*len(decomp)\n",
    "for cur in decomp:\n",
    "    subplot += 1\n",
    "    plt.figure()\n",
    "    nx.draw(cur)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}