Add sage code

lib/vertex_coloring.py

@@ -0,0 +1,11 @@
+"""Utilities for verifying vertex colorings."""
+from typing import Any, cast
+from sage.all import Graph
+
+def check_vertex_coloring(graph: Graph, vertex_coloring: dict[Any, int]) -> bool:
+    """Raise ValueError if any two adjacent vertices share a color."""
+    for v in cast(list[Any], graph.vertices()):  # type: ignore
+        for nv in cast(list[Any], graph.neighbors(v)):  # type: ignore
+            if vertex_coloring[nv] == vertex_coloring[v]:
+                raise ValueError(f"Color {nv} equal to color {v}")
+    return True