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An Improvement of Hind's Upper Bound on the Total Chromatic Number

Published online by Cambridge University Press:  12 September 2008

Amanda Chetwynd  and
Roland Häggkvist
Amanda Chetwynd
Affiliation:
Department of Mathematics, University of Lancaster, Lancaster LAI 4YF, UK
Roland Häggkvist
Affiliation:
Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden
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Abstract

We show that the total chromatic number of a simple k-chromatic graph exceeds the chromatic index by at most 18k ⅓ log ½ 3k.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 2 , June 1996 , pp. 99 - 104
Copyright
Copyright © Cambridge University Press 1996

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References

[1]H. Chernoff, H. (1952) A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals Math. Statist. 23 493–509.CrossRefGoogle Scholar
[2]Chetwynd, A. G. and Häggkvist, R. (1992) Some upper bounds on the total and list chromatic numbers of multigraphs. J. Graph Theory 16(5) 503–516.Google Scholar
[3]Erdös, P. and Lovász, L. (1973) Problems and results on 3-chromatic hypergraphs and some related questions. In Colloquia Mathematica Societatis János Bolyai 10. Infinite and finite sets, Keszthely, Hungary (Hajnal, A., Rado, R. and Sós, V. T., eds.). North-Holland, 609–627.Google Scholar
[4]Häggkvist, R. and Thomason, A. G. (1993) Oriented hamilton cycles in digraphs. Research report no. 1, Department of Mathematics, University of Umeå, Sweden.Google Scholar
[5]Hind, H. (1988) Restricted edge-colourings. Doctoral Thesis, Peterhouse College, Cambridge, UK.Google Scholar
[6]Hind, H. (1990) An upper bound for the total chromatic number. Graphs and Combinatorics 6 153–160.CrossRefGoogle Scholar
[7]Lovász, L. (1979) Combinatorial Problems and Exercises. North-Holland.Google Scholar
[8]Spencer, J. (1987) Ten Lectures on the Probabilistic Method. SIAM, Philadelphia, PA.Google Scholar
[9]Vizing, V. G. (1964) On an estimate of the chromatic class of a p-graph. Diskret Analiz. 3 25–30 (in Russian).Google Scholar