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Discussiones Mathematicae Graph Theory 24(1) (2004) 125-135
DOI: https://doi.org/10.7151/dmgt.1219
A NOTE ON TOTAL COLORINGS OF PLANAR GRAPHS WITHOUT 4-CYCLES
| Ping Wang
Department of Mathematics, Statistics and Computer Science |
Jian-Liang Wu
School of Mathematics, Shandong University |
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.
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Received 26 February 2002
Revised 21 October 2003