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

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 53, Issue 1, 2016, pp.139-151
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2016.53.1.139

Title & Authors

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

Tan, Xiang;

Tan, Xiang;

Abstract

A k-total-coloring of a graph G is a coloring of 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 k-total-coloring. Let G be a planar graph with maximum degree . In this paper, it`s proved that if and G does not contain adjacent 5-cycles, then the total chromatic number is .

Keywords

planar graph;total coloring;adjacent 5-cycle;

Language

English

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