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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author shellac
date Mon, 22 Mar 2021 18:12:50 +0000
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Ramsey numbers.
import networkx as nx
from ...utils import arbitrary_element

__all__ = ["ramsey_R2"]

def ramsey_R2(G):
    r"""Compute the largest clique and largest independent set in `G`.

    This can be used to estimate bounds for the 2-color
    Ramsey number `R(2;s,t)` for `G`.

    This is a recursive implementation which could run into trouble
    for large recursions. Note that self-loop edges are ignored.

    G : NetworkX graph
        Undirected graph

    max_pair : (set, set) tuple
        Maximum clique, Maximum independent set.
    if not G:
        return set(), set()

    node = arbitrary_element(G)
    nbrs = (nbr for nbr in nx.all_neighbors(G, node) if nbr != 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())

    # 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)