Maximal Independent Set Based Approach for Graph Coloring Problem

Graph coloring problem is a well-known NP-complete problem and there are many approaches proposed to solve this problem. For a graph coloring algorithm to be efficient, it must color the input graph with minimum colors and must also find the solution in the minimum possible time. Heuristic approaches emphasize on the time complexity while the exact approaches concentrate on the number of colors used. Here, we proposed an approach which solves the graph coloring problem more efficiently by providing minimum number of colors with effectively lesser time than that of the fastest exact algorithm till date. In our approach, we exploit the concept of maximal independent sets using trees. We tested our algorithm on various DIMACS graphs (up to 10000 vertices) and found the results (in terms of time and colors) much more efficient than the existing.