Some upper bounds on the list and total chromatic numbers of multigraphs.

Haggkvist, Roland A. and Chetwynd, Amanda G. (1992) Some upper bounds on the list and total chromatic numbers of multigraphs. Journal of Graph Theory, 16 (5). pp. 503-516. ISSN 0364-9024

Abstract

In this paper we discuss some estimates for upper bounds on a number of chromatic parameters of a multigraph. In particular, we show that the total chromatic number for an n-order multigraph exceeds the chromatic index by the smallest t such that t! > n.