This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

Source code for networkx.algorithms.approximation.ramsey

# -*- coding: utf-8 -*-
Ramsey numbers.
#   Copyright (C) 2011 by
#   Nicholas Mancuso <nick.mancuso@gmail.com>
#   All rights reserved.
#   BSD license.
import networkx as nx
from ...utils import arbitrary_element

__all__ = ["ramsey_R2"]
__author__ = """Nicholas Mancuso (nick.mancuso@gmail.com)"""

[docs]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 = arbitrary_element(G) nbrs = nx.all_neighbors(G, node) nnbrs = nx.non_neighbors(G, node) c_1, i_1 = ramsey_R2(G.subgraph(nbrs).copy()) c_2, i_2 = ramsey_R2(G.subgraph(nnbrs).copy()) c_1.add(node) i_2.add(node) # Choose the larger of the two cliques and the larger of the two # independent sets, according to cardinality. return max(c_1, c_2, key=len), max(i_1, i_2, key=len)