Efficient self-stabilizing grundy coloring algorithms

A coloring of a graph is an assignment of colors to its nodes so that no two adjacent nodes are assigned the same color. Given a graph G, by a Grundy k-coloring of G mean any proper k-vertex coloring of G such that for each two colors i and j, i< j, every vertex of G colored by j has a neighbor with color i. The maximum k for which there exists a Grundy k-coloring is denoted by Γ (G) and called Grundy (chromatic) number of G. In this paper the authors introduce Grundy colorings and the authors give two algorithms to maintain the Grundy coloring of any graph G when a changement has been occurred (an edge is added or broken).