From 4a52a71956a8d46fcb7294ac71734504bb09bcc2 Mon Sep 17 00:00:00 2001
From: S. Solomon Darnell
Date: Fri, 28 Mar 2025 21:52:21 -0500
Subject: two version of R2R are here

---
 .../networkx/algorithms/approximation/ramsey.py    | 53 ++++++++++++++++++++++
 1 file changed, 53 insertions(+)
 create mode 100644 .venv/lib/python3.12/site-packages/networkx/algorithms/approximation/ramsey.py

(limited to '.venv/lib/python3.12/site-packages/networkx/algorithms/approximation/ramsey.py')

diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/approximation/ramsey.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/approximation/ramsey.py
new file mode 100644
index 00000000..0552e4a9
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/approximation/ramsey.py
@@ -0,0 +1,53 @@
+"""
+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)
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