Source code for networkx.algorithms.approximation.ramsey

Ramsey numbers.
import networkx as nx
from networkx.utils import not_implemented_for

from ...utils import arbitrary_element

__all__ = ["ramsey_R2"]

[docs] @not_implemented_for("directed") @not_implemented_for("multigraph") @nx._dispatchable 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. Parameters ---------- G : NetworkX graph Undirected graph Returns ------- max_pair : (set, set) tuple Maximum clique, Maximum independent set. Raises ------ NetworkXNotImplemented If the graph is directed or is a multigraph. """ 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()) 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)