Acyclic Coloring of Graphs with Maximum Degree 7

被引：5

作者：

Wang, Juan ^{[1
,2
,3
]}

Miao, Lianying ^{[2
]}

Song, Wenyao ^{[4
]}

Liu, Yunlong ^{[5
]}

机构：

[1] Qufu Normal Univ, Sch Management, Rizhao 276826, Peoples R China

[2] China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China

[3] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

[4] Zaozhuang Univ, Sch Math & Stat, Zaozhuang 277160, Peoples R China

[5] Qufu Normal Univ, Sch Engn, Rizhao 276826, Peoples R China

来源：

GRAPHS AND COMBINATORICS | 2021年 / 37卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Graph coloring; Acyclic coloring; Maximum degree; Regular graph;

D O I：

10.1007/s00373-020-02254-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The acyclic chromatic number a(G) of a graph G is the minimum number of colors such that G has a proper vertex coloring and no bichromatic cycles. For a graph G with maximum degree Delta, Grunbaum (1973) conjectured a(G) <= Delta 1. Up to now, the conjecture has only been shown for Delta <= 4. In this paper, it is proved that a(G) <= 12 for Delta = 7, thus improving the result a(G) <= 17 of Dieng et al. (in: Proc. European conference on combinatorics, graph theory and applications, 2010).

引用

页码：455 / 469

页数：15

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