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Total chromatic number of complete r-partite graphs

✍ Scribed by K. H. Chew; H. P. Yap

Publisher: John Wiley and Sons
Year: 1992
Tongue: English
Weight: 284 KB
Volume: 16
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190160608

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✦ Synopsis

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.

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