The achromatic indices of the regular complete multipartite graphs Original Research Article

In this paper, we study the achromatic indices of the regular complete multipartite graphs and obtain the following results: 1. (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. (2) An improved Bouchet coloring which gives the achromatic indices of another infinite family of regular complete multipartite graphs.