Elsevier

Discrete Applied Mathematics

Volume 171, 10 July 2014, Pages 116-121
Discrete Applied Mathematics

Total colorings of planar graphs without chordal 6-cycles

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Abstract

A total k-coloring of a graph G is a coloring of V(G)E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number of G is the smallest integer k such that G has a total k-coloring. In this paper, it is proved that if G is a planar graph with maximum degree Δ7 and without chordal 6-cycles, then the total chromatic number of G is Δ+1.

Keywords

Total coloring
Planar graph
Cycle
Chords

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This work is supported by the National Natural Foundation of China (No. 11271006) and the Natural Science Foundation of Shandong Province (ZR2012AL08).