On -acyclic edge colorings of planar graphs

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• 作者：Xin Zhang^a ; ^b ; ^{sdu.zhang@yahoo.com.cn} ; ^{xinzhang@mail.sdu.edu.cn} ; Guanghui Wang^a ; ^{ghwang@sdu.edu.cn} ; Yong Yu^a ; ^{yuyong6834@yahoo.com.cn} ; Jinbo Li^c ; ^{lijinbo@cumt.edu.cn} ; Guizhen Liu^a ; ^{gzliu@sdu.edu.cn}
• 关键词：r-acyclic edge coloring ; Planar graph ; Series&ndash ; parallel graph ; Outerplanar graph
• 刊名：Discrete Applied Mathematics
• 出版年：2012
• 期刊代码：46_0166218x
• 类别：cp
• 出版时间：September, 2012
• 卷：160
• 期：13-14
• 页码：2048-2053
• 文件大小：229 K

摘要

A proper edge coloring of is -acyclic if every cycle contained in is colored with at least colors. The -acyclic chromatic index of a graph, denoted by , is the minimum number of colors required to produce an -acyclic edge coloring. In this paper, we study 4-acyclic edge colorings by proving that for every planar graph, for every series-parallel graph and for every outerplanar graph. In addition, we prove that every planar graph with maximum degree at least and girth at least has for every .