On Total Colorings of Some Special 1-planar Graphs

被引：0

作者：

Lin SUN ^{[1
,2
]}

Jian-liang WU ^{[1
]}

Hua CAI ^{[1
,2
]}

机构：

[1] Department of Mathematics, Changji University

[2] School of Mathematics, Shandong University

来源：

Acta Mathematicae Applicatae Sinica | 2017年 / 33卷 / 03期

关键词：

1-planar graph; total coloring; discharging method; girth; r-minimal graph;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

摘要：

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either ?(G) ≥ 9 and g(G) ≥ 4, or ?(G) ≥ 7 and g(G) ≥ 5, where ?(G) is the maximum degree of G and g(G) is the girth of G.

引用

页码：607 / 618

页数：12

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