A Tree Based Novel Approach for Graph Coloring Problem Using Maximal Independent Set

Abstract

Graph coloring problem is a famous NP-complete problem and there exist several methods which have been projected to resolve this issue. For a graph colouring algorithm to be efficient, it ought to paint the input graph by minimum colours and must also find the solution in the minimum possible time. Here, we have proposed a different method to solve the graph coloring problem using maximal independent set. In our method, we used the concept of maximal independent sets using trees. In the first part, it converts a massive graph into a sequence of step by step smaller graphs by eliminating big independent sets from the initial graph. The second part starts by assigning a proper colour to each maximal independent set within the sequence. The proposed method is estimated on the DIMACS standards and presented reasonable outcomes concerning to other latest methods.