Total chromatic number of complete  r ‐partite graphs | Zendy

Chew K. H. | Zendy; Yap H. P. | Zendy

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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.

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