52 lines
1.3 KiB
Python
52 lines
1.3 KiB
Python
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"""
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Ramsey numbers.
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"""
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import networkx as nx
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from networkx.utils import not_implemented_for
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from ...utils import arbitrary_element
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__all__ = ["ramsey_R2"]
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@not_implemented_for("directed")
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@not_implemented_for("multigraph")
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def ramsey_R2(G):
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r"""Compute the largest clique and largest independent set in `G`.
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This can be used to estimate bounds for the 2-color
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Ramsey number `R(2;s,t)` for `G`.
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This is a recursive implementation which could run into trouble
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for large recursions. Note that self-loop edges are ignored.
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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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Raises
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------
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NetworkXNotImplemented
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If the graph is directed or is a multigraph.
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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 = (nbr for nbr in nx.all_neighbors(G, node) if nbr != 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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