public static int VertexColoring(this Graph graph, out int[] colors)
        {
            if (graph.Directed)
                throw new ArgumentException();

            if (0 == graph.VerticesCount)
            {
                colors = new int[0];
                return 0;
            }

            int maxColour = 0;
            int[] vertexColors = new int[graph.VerticesCount];

            for (int i = 0; i < vertexColors.Length; i++)
            {
                vertexColors[i] = -1;   //vertex not colored yet
            }

            int[] usedColors = new int[graph.VerticesCount];
            int color = 0;

            for (int v = 0; v < graph.VerticesCount; v++)
            {
                Array.Clear(usedColors, 0, usedColors.Length);

                color = 0;
                foreach (var e in graph.OutEdges(v))
                {
                    if (-1 != vertexColors[e.To])
                    {
                        color = vertexColors[e.To];
                        usedColors[color] = 1;     //colour used
                    }
                }

                for (int i = 0; i < usedColors.Length; i++)
                {
                    if (0 == usedColors[i])
                    {
                        vertexColors[v] = i;

                        if (i > maxColour)  //for count of all colours
                        {
                            maxColour = i;
                        }

                        break;
                    }

                    //int minColour = 0; bool foundMinColour = false;

                    //while (!foundMinColour)
                    //{
                    //    foundMinColour = true;
                    //    foreach (var e in graph.OutEdges(v))
                    //    {
                    //        if (vertexColors[e.To] == minColour)
                    //        {
                    //            minColour++;
                    //            foundMinColour = false;
                    //            break;
                    //        }
                    //    }
                    //}

                    //if (minColour > maxColour)
                    //{
                    //    maxColour = minColour;
                    //}

                    //vertexColors[v] = minColour;
                }
            }

            colors = vertexColors;
            return maxColour + 1;
        }