THE ACHROMATIC INDEXES OF THE REGULAR COMPLETE MULTIPARTITE GRAPHS

Abstract

In this paper, we study the achromatic indices of the regular complete multipartite graphs and obtain the following results: (1) A good upper bound for the achromatic index of the regular complete multipartite graph which gives the exact values of an infinite family of graphs and solves a problem posed by Bouchet. (2) An improved Bouchet coloring which gives the achromatic indices of another infinite family of regular complete multipartite graphs.