int ChromaticNumber(Graph G)
{
    for (int i = 0; i < G.Vertices.size(); ++i)
    {
        //initialize vertex color to 1
        ++G.Vertices[i].Color;
        bool Match = true;

        //loop while there is an adjacent vertex with the same color
        while (Match)
        {
            Match = false;
            for (int j = 0; j < G.Vertices[i].Edges.size(); ++j)
            {
                //get adjacent vertex
                int AdjacentVertex = G.Vertices[i].Edges[j];

                //if an adjacent vertex has the same color, increment the
                //current vertex's color
                if (G.Vertices[i].Color == G.Vertices[AdjacentVertex].Color)
                {
                    ++G.Vertices[i].Color;
                    Match = true;
                }
            }
        }
    }

    int MaxColor = 0;

    //loop to determine the largest color value
    for (int i = 0; i < G.Vertices.size(); ++i)
        if (G.Vertices[i].Color > MaxColor)
            MaxColor = G.Vertices[i].Color;

    return MaxColor;
}