[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2016.53.1.139

TOTAL COLORINGS OF PLANAR GRAPHS WITH MAXIMUM DEGREE AT LEAST 7 AND WITHOUT ADJACENT 5-CYCLES

Tan, Xiang (School of Mathematics and Quantitative Economics Shandong University of Finance and Economics)

Publication Information

Bulletin of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 139-151 More about this Journal

Abstract

A k-total-coloring of a graph G is a coloring of $V{\cup}E$ using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number ${\chi}^{{\prime}{\prime}}(G)$ of G is the smallest integer k such that G has a k-total-coloring. Let G be a planar graph with maximum degree ${\Delta}$ . In this paper, it's proved that if ${\Delta}{\geq}7$ and G does not contain adjacent 5-cycles, then the total chromatic number ${\chi}^{{\prime}{\prime}}(G)$ is ${\Delta}+1$ .

Keywords

planar graph; total coloring; adjacent 5-cycle;

Citations & Related Records

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