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Total chromatic number of graphs of high degree

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

H. P. Yap ,
Wang Jian-Fang  and
Zhang Zhongfu
H. P. Yap
Affiliation:
Department of Mathematics, National University of Singapore10 Kent Ridge CrescentSingapore0511
Wang Jian-Fang
Affiliation:
Institute of Applied MathematicsAcademia Sinica Beijing The People'sRepublic of China
Zhang Zhongfu
Affiliation:
Department of Mathematics, Lanzhou Railway InstituteLanzhou, Gansu The People's Republic of China
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Abstract

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Using a new proof technique of the first author (by adding a new vertex to a graph and creating a total colouring of the old graph from an edge colouring of the new graph), we prove that the TCC (Total Colouring Conjecture) is true for any graph G of order n having maximum degree at least n - 4. These results together with some earlier results of M. Rosenfeld and N. Vijayaditya (who proved that the TCC is true for graphs having maximum degree at most 3), and A. V. Kostochka (who proved that the TCC is true for graphs having maximum degree 4) confirm that the TCC is true for graphs whose maximum degree is either very small or very big.

MSC classification

Secondary: 05C15: Coloring of graphs and hypergraphs
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 3 , December 1989 , pp. 445 - 452
Copyright
Copyright © Australian Mathematical Society 1989

References

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