Total Colourings of Graphs

Abstract

We prove that the TCC (Total Colouring Conjecture) is true for complete r-partite graphs, which extends a result of M. Rosenfeld. We also give an alternative, slightly simpler proof of an earlier result (which says that the TCC is true for graphs having maximum degree 3) obtained independently by M. Rosenfeld and N. Vijayaditya.