Strict Strong Graph Coloring: Algorithms and Applications

This paper addresses a recent combinatorial optimization problem called the Strict Strong graph coloring. This new coloring parameter investigates the use of dominance relation between graph vertices and color classes. This kind of coloring has been defined by Haddad and Kheddouci. It consists in properly coloring the graph in a way each vertex dominates at least one color class. In this paper, we recall some fundamental concepts, bounds and theorems related to the strict strong coloring. Also, we show its usefulness to deal with real world applications and we provide a critical review of the existing approaches dealing with such NP complete problem.