DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 24(1) (2004) 125-135
DOI: 10.7151/dmgt.1219

A NOTE ON TOTAL COLORINGS OF PLANAR GRAPHS WITHOUT 4-CYCLES

Ping Wang

Department of Mathematics, Statistics and Computer Science
St. Francis Xavier University, Antigonish, Nova Scotia, Canada
e-mail: pwang@stfx.ca

Jian-Liang Wu

School of Mathematics, Shandong University
Jinan, Shandong, 250100, P.R. China

Abstract

Let G be a 2-connected planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the total chromatic number of G is Δ +1 if (Δ ,k)∈ {(7,4),(6,5),(5,7),(4,14)}.

Keywords: total coloring, planar graph, list coloring, girth.

2000 Mathematics Subject Classification: 05C15.

References

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Received 26 February 2002
Revised 21 October 2003