"""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