A tree-based graph coloring algorithm using independent set

Abstract

This paper introduces a tree data structure-based graph coloring algorithm. Algorithm explores vertices in the tree form to finds maximal independent set, than these independent sets are colored with minimum colors. Proposed algorithm is tested on various DIMACS standard of graph instances. Algorithm is design to solve graph coloring problem for high degree graphs, i.e. the proposed algorithm is highly efficient for those graphs which has number of edges to number of vertices ratio is very high. Worst and best case time complexity of proposed algorithm is also discussed in this paper.