An Upper Bound for the Total Chromatic Number H.R. Hind* Department of Pure Mathematics, University of Cambridge, 16 Mill Lane, Cambridge, England
Abstract. The total chromatic number, Z"(G),of a graph G, is defined to be the minimum number
ofcolours needed to colour the vertices and edges of a graph in such a way that no adjacent vertices, no adjacent edges and no incident vertex and edge are given the same colour. This paper shows that )('(G) _