Optimal acyclic edge-coloring of cubic graphs

被引：13

作者：

Andersen, Lars Dovling ^{[1
]}

Macajova, Edita ^{[2
]}

Mazak, Jan ^{[2
]}

机构：

[1] Aalborg Univ, Dept Math Sci, DK-9220 Aalborg SO, Denmark

[2] Comenius Univ, Fac Math Phys & Informat, Dept Comp Sci, Bratislava 84248, Slovakia

来源：

JOURNAL OF GRAPH THEORY | 2012年 / 71卷 / 04期

关键词：

acyclic edge-coloring; cubic graphs;

D O I：

10.1002/jgt.20650

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An acyclic edge-coloring of a graph is a proper edge-coloring such that the subgraph induced by the edges of any two colors is acyclic. The acyclic chromatic index of a graph G is the smallest number of colors in an acyclic edge-coloring of G. We prove that the acyclic chromatic index of a connected cubic graph G is 4, unless G is K4 or K3,3; the acyclic chromatic index of K4 and K3,3 is 5. This result has previously been published by Fiamcik, but his published proof was erroneous.

引用

页码：353 / 364

页数：12

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