43 lines
1.0 KiB
Python
43 lines
1.0 KiB
Python
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# -*- coding: utf-8 -*-
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"""
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Ramsey numbers.
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"""
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# Copyright (C) 2011 by
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# Nicholas Mancuso <nick.mancuso@gmail.com>
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# All rights reserved.
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# BSD license.
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import networkx as nx
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from ...utils import arbitrary_element
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__all__ = ["ramsey_R2"]
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__author__ = """Nicholas Mancuso (nick.mancuso@gmail.com)"""
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def ramsey_R2(G):
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r"""Approximately computes the Ramsey number `R(2;s,t)` for graph.
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Parameters
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----------
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G : NetworkX graph
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Undirected graph
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Returns
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-------
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max_pair : (set, set) tuple
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Maximum clique, Maximum independent set.
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"""
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if not G:
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return set(), set()
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node = arbitrary_element(G)
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nbrs = nx.all_neighbors(G, node)
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nnbrs = nx.non_neighbors(G, node)
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c_1, i_1 = ramsey_R2(G.subgraph(nbrs).copy())
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c_2, i_2 = ramsey_R2(G.subgraph(nnbrs).copy())
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c_1.add(node)
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i_2.add(node)
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# Choose the larger of the two cliques and the larger of the two
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# independent sets, according to cardinality.
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return max(c_1, c_2, key=len), max(i_1, i_2, key=len)
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