List edge and list total colorings of planar graphs without short cycles

Authors:
Bin Liu;Jianfeng Hou;Guizhen Liu
Affiliations:
School of Mathematics, Shandong University, Jinan, Shandong 250100, P.R. China;School of Mathematics, Shandong University, Jinan, Shandong 250100, P.R. China;School of Mathematics, Shandong University, Jinan, Shandong 250100, P.R. China
Venue:
Information Processing Letters
Year:
2008

Citing 6
Cited 2

Some upper bounds on the total and list chromatic numbers of multigraphs

Journal of Graph Theory
The list chromatic index of a bipartite multigraph

Journal of Combinatorial Theory Series B
List edge and list total colourings of multigraphs

Journal of Combinatorial Theory Series B
Choosability, edge choosability, and total choosability of outerplane graphs

European Journal of Combinatorics
New Bounds on the List-Chromatic Index of the Complete Graph and Other Simple Graphs

Combinatorics, Probability and Computing
Graph Theory With Applications

Graph Theory With Applications

Note: Total coloring of planar graphs without 6-cycles

Discrete Applied Mathematics
Note: A structural theorem for planar graphs with some applications

Discrete Applied Mathematics

Quantified Score

Hi-index	0.89

Visualization

Abstract

Let G be a planar graph with maximum degree @D(G). We use @g"l^'(G) and @g"l^''(G) to denote the list edge chromatic number and list total chromatic number of G, respectively. In this paper, it is proved that @g"l^'(G)=@D(G) and @g"l^''(G)=@D(G)+1 if @D(G)=6 and G has neither C"4 nor C"6, or @D(G)=7 and G has neither C"5 nor C"6, where C"k is a cycle of length k.