A linked list-based exact algorithm for graph coloring problem

Abstract

Graph coloring is an NP-hard problem. There is ample room to further reduce the number of colors being used under the strict constraints of the problem. This paper proposes an algorithm that stores the information of the vertices in the graph, together with the color and the next address field of a node in a singly linked list. The coloring of a particular vertex is decided on the content of color field of node corresponding to the searched vertex for coloring. The adjacency matrix of the graph was adopted to select the feasible color to be allocated to a vertex, without violating the constraints for coloring of the vertices in the graph. The proposed algorithm was tested on DIMACS benchmark graphs, using Python 3.6. The results show that our algorithm produced the result with the optimal number of colors required to solve the problem. This research provides a new strategy to find the optimal coloring solution for each type of graphs.