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# -*- coding: utf-8 -*-
"""
Ramsey numbers.
"""
# Copyright (C) 2011 by
# Nicholas Mancuso <nick.mancuso@gmail.com>
# All rights reserved.
# BSD license.
import networkx as nx
__all__ = ["ramsey_R2"]
__author__ = """Nicholas Mancuso (nick.mancuso@gmail.com)"""
def ramsey_R2(G):
r"""Approximately computes the Ramsey number `R(2;s,t)` for graph.
Parameters
----------
G : NetworkX graph
Undirected graph
Returns
-------
max_pair : (set, set) tuple
Maximum clique, Maximum independent set.
"""
if not G:
return (set([]), set([]))
node = next(G.nodes_iter())
nbrs = nx.all_neighbors(G, node)
nnbrs = nx.non_neighbors(G, node)
c_1, i_1 = ramsey_R2(G.subgraph(nbrs))
c_2, i_2 = ramsey_R2(G.subgraph(nnbrs))
c_1.add(node)
i_2.add(node)
return (max([c_1, c_2]), max([i_1, i_2]))
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