List edge and list total colorings of planar graphs without 6-cycles with chord

Aijun Dong; Guizhen Liu; Guojun Li

doi:10.4134/BKMS.2012.49.2.359

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Bull. Korean Math. Soc. 2012; 49(2): 359-365

Printed March 1, 2012

https://doi.org/10.4134/BKMS.2012.49.2.359

List edge and list total colorings of planar graphs without 6-cycles with chord

Aijun Dong, Guizhen Liu, and Guojun Li

Shandong University, Shandong University, Shandong University

Abstract

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Abstract

Giving a planar graph $G$, let $\chi'_l(G)$ and $\chi''_l(G)$ denote the list edge chromatic number and list total chromatic number of $G$ respectively. It is proved that if a planar graph $G$ without 6-cycles with chord, then $\chi'_l(G)\leq\Delta(G)+1$ and $\chi''_l(G)\leq\Delta(G)+2$ where $\Delta(G)\geq6$.

Keywords: list coloring, planar graph, choosability

MSC numbers: 05C15