Total chromatic number of complete r‐partite graphs

Abstract

Abstract Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete r ‐partite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete r ‐partite graph. Rosenfeld's result had been generalized recently to complete r ‐partite graphs by Yap (1989). The main result of this paper is to prove that the total chromatic number of every complete r ‐partite graph G of odd order is Δ ( G ) + 1. This result gives a partial generalization of Bermond's theorem.