不含4-,6-圈和相交三角形的平面图的无圈边色数  

The Acyclic Chromatic Index of Planar Graphs Without 4-,6-cycles and Intersecting Triangles

作　　者：卜月华 贾琪[1] 朱洪国 BU Yuehua;JIA Qi;ZHU Hongguo(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China;Xingzhi College,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华321004 [2]浙江师范大学行知学院,浙江金华321004

出　　处：《数学进展》2023年第6期991-1004,共14页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.11771403,11871439)

摘　　要：图G的一个边染色φ:E(G)→{1,2,…,k},若满足任意相邻边都染不同的颜色,且图G不存在双色圈,则称φ为图G的一个无圈k-边染色.图G的无圈边色数χ’_(α)(G)为使得图G有一个无圈k-边染色的最小正整数k.本文主要证明了对于无4-,6-圈且3-圈与3-圈不相交的平面图G,若Δ(G)≥9,则χ’_(α)(G)≤Δ(G)+1.A proper edge k-coloring is a mappingφ:E(G)→{1,2,…,k}such that any two adjacent edges receive different colors.A proper edge k-coloringφof G is called acyclic if there are no bichromatic cycles in G.The acyclic chromatic index of G,denoted byχ'_(α)(G),is the smallest integer k such that G is acyclically edge k-colorable.In this paper,we show that if G is a plane graph without 4-,6-cycles and intersecting 3-cycles,Δ(G)≥9,thenχ'_(α)(G)≤Δ(G)+1.

关 键 词：无圈边染色 平面图 圈 

分 类 号：O157.5[理学—数学]