Total coloring of planar graphs without adjacent chordal 6-cycles

Huijuan Wang, Bin Liu (), Xiaoli Wang, Guangmo Tong, Weili Wu and Hongwei Gao
Additional contact information
Huijuan Wang: Qingdao University
Bin Liu: Ocean University of China
Xiaoli Wang: Ocean University of China
Guangmo Tong: University of Texas at Dallas
Weili Wu: University of Texas at Dallas
Hongwei Gao: Qingdao University

Journal of Combinatorial Optimization, 2017, vol. 34, issue 1, No 18, 257-265

Abstract: Abstract A total coloring of a graph G is a coloring such that no two adjacent or incident elements receive the same color. In this field there is a famous conjecture, named Total Coloring Conjecture, saying that the the total chromatic number of each graph G is at most $$\Delta +2$$ Δ + 2 . Let G be a planar graph with maximum degree $$\Delta \ge 7$$ Δ ≥ 7 and without adjacent chordal 6-cycles, that is, two cycles of length 6 with chord do not share common edges. In this paper, it is proved that the total chromatic number of G is $$\Delta +1$$ Δ + 1 , which partly confirmed Total Coloring Conjecture.

Keywords: Planar graph; Total coloring; Cycle (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0063-3

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