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+"""
+Ramsey numbers.
+"""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+from ...utils import arbitrary_element
+
+__all__ = ["ramsey_R2"]
+
+
+@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)