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List-colouring in IPython using Vizing.
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{ | |
"metadata": { | |
"name": "" | |
}, | |
"nbformat": 3, | |
"nbformat_minor": 0, | |
"worksheets": [ | |
{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"List-colouring in Python with Vizing\n", | |
"====================================\n", | |
"by Matthew Henderson\n", | |
"\n", | |
"Last updated: Thu Nov 21 23:10:18 GMT 2013.\n", | |
"\n", | |
"This notebook introduces the ``vizing`` Python package for colouring graphs. The main focus of ``vizing`` is on list-colourings but total-colourings and colourings of vertices and edges without lists are also supported.\n", | |
"\n", | |
"This notebook can be viewed at: [http://nbviewer.ipython.org/5857920](http://nbviewer.ipython.org/5857920).\n", | |
"\n", | |
"The source code for this notebook can be found at: [https://gist.github.com/MHenderson/5857920](https://gist.github.com/MHenderson/5857920)\n", | |
"\n", | |
"In Section 1, we introduce colouring the vertices of a graph when each vertex has a list of prescribed colours. In Section 2 list-edge-colouring is discussed." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"import random\n", | |
"random.seed(0)\n", | |
"\n", | |
"def standard_colours(G):\n", | |
" return [G.node[node]['color'] for node in G.node.keys()]" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 1 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"1. List Vertex-Colouring\n", | |
"------------------------" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"import networkx as nx\n", | |
"from vizing.colouring import InOrder, RandomAvailableColor, vertex_coloring" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 2 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"G = nx.complete_graph(4)\n", | |
"for node in G.node:\n", | |
" G.node[node]['list'] = range(4)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 3 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"vertex_coloring(G, nodes = InOrder, choose_color = RandomAvailableColor)\n", | |
"nx.draw_circular(G, node_color = standard_colours(G))" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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5H9/hykV79uxRQcH5Ki29SFK8Tx8fVm7ur3XbbVO1ZMkSjRs3Tg8++KC6devW/q1AC3yH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\n/wOedQ+aqTWX/wAAAABJRU5ErkJggg==\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x302ca10>" | |
] | |
} | |
], | |
"prompt_number": 4 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The next example is completing a Shidoku puzzle." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"A = { 0: [1,2,3,4,5,8,12],\n", | |
" 1: [2,3,4,5,9,13],\n", | |
" 2: [3,6,7,10,14],\n", | |
" 3: [6,7,11,15],\n", | |
" 4: [5,6,7,8,12],\n", | |
" 5: [6,7,9,13],\n", | |
" 6: [7,10,14],\n", | |
" 7: [11,15],\n", | |
" 8: [9,10,11,12,13],\n", | |
" 9: [10,11,12,13],\n", | |
" 10: [11,14,15],\n", | |
" 11: [15],\n", | |
" 12: [13,14,15],\n", | |
" 13: [14,15],\n", | |
" 14: [15] }\n", | |
"G = nx.from_dict_of_lists(A)\n", | |
"L = { 0: [1],\n", | |
" 1: [2],\n", | |
" 2: [3],\n", | |
" 3: [4],\n", | |
" 4: [3],\n", | |
" 5: [4],\n", | |
" 6: [1],\n", | |
" 7: [2],\n", | |
" 8: [2, 4],\n", | |
" 9: [1],\n", | |
" 10: [4],\n", | |
" 11: [3],\n", | |
" 12: [3, 4],\n", | |
" 13: [3],\n", | |
" 14: [2],\n", | |
" 15: [1, 4]}\n", | |
"for node in G.node:\n", | |
" G.node[node]['list'] = L[node]\n", | |
"vertex_coloring(G, nodes = InOrder, choose_color = RandomAvailableColor)\n", | |
"nx.draw_circular(G, node_color = standard_colours(G))" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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dHTZu3JgzZ87kpUuXSn2ssqRVcGpqKp2cnLhv3z6Gh4ezU6dOBX6BK8yuXbtY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\nfXtOm1a8D6dLly5xwIAB1NfXp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wtGjx6NWrVqKTTgKj8k8eLFC9y9exd3797FnTt3kdYk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\nBUEQBKGcifAVBEEQhP+PzgAAsA5c88Ga9QwAAAAASUVORK5CYII=\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x302cbd0>" | |
] | |
} | |
], | |
"prompt_number": 5 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"2. List Edge-Colouring\n", | |
"----------------------" | |
] | |
} | |
], | |
"metadata": {} | |
} | |
] | |
} |
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