Add sage code

lib/coloring.py

@@ -0,0 +1,19 @@
+"""Utilities for converting integer colorings to named colors."""
+from typing import Any
+
+COLORS = ['blue', 'red', 'green', 'yellow', 'purple']
+
+def convert_coloring(
+    coloring: dict[Any, int],
+    vertices: list[Any] | None = None
+) -> dict[str, list[Any]]:
+    """Convert an integer coloring dict to a dict mapping color names to vertex lists."""
+    colors: dict[str, list[Any]] = {}
+    for k, v in coloring.items():
+        if vertices and k not in vertices:
+            continue
+        color = COLORS[v]
+        if color not in colors:
+            colors[color] = []
+        colors[color].append(k)
+    return colors