A study of the total chromatic number of equibipartite graphs

Abstract

The total chromatic number chi(t)(G) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same color, no incident edges receive the same color as either of the vertices it is incident with. In this paper, we obtain some results of the total chromatic number of the equibiparrite graphs of order 2n with maximum degree n - 1. As a part of our results, we disprove the biconformability conjecture. (C) 1998 Published by Elsevier Science B.V. All rights reserved.