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Total chromatic number of complete r ‐partite graphs
Author(s) -
Chew K. H.,
Yap H. P.
Publication year - 1992
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190160608
Subject(s) - mathematics , combinatorics , chromatic scale , conjecture , graph , generalization , brooks' theorem , discrete mathematics , total coloring , 1 planar graph , chordal graph , graph power , line graph , mathematical analysis
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.