不含3-圈的平面图的弱邻点可区别边染色  

Weak adjacent vertex distinguishing edge coloring of planar graphs without 3-cycles

作　　者：何正月 梁立[1] 高炜[1] HE Zheng-yue;LIANG Li;GAO Wei(School of Information Science and Technology,Yunnan Normal University,Kunming 650500,Yunnan,China)

机构地区：[1]云南师范大学信息学院,云南昆明650500

出　　处：《云南大学学报（自然科学版）》2023年第6期1171-1178,共8页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(1216094).

摘　　要：弱邻点可区别边染色是指图G有一个正常边染色且任意2个相邻的最大度顶点的颜色集合不相等.使图G有一个弱邻点可区别边染色的最小颜色数值,被称为弱邻点可区别边色数,记作χ′_(a△)(G)证明了:若图G是不含3-圈的平面图,则有χ′_(a△)(G)≤max{9,△(G)+1}.The weak adjacent vertex distinguishing edge coloring of graph G is a proper edge coloring of G such that any pair of adjacent maximum degree vertices have distinct sets of colors.The minimum number of colors required for a weak adjacent vertex distinguishing edge coloring of Gis denoted by χ′_(a△)(G).In this paper,we prove that if G is a planar graph without 3-cycles,then χ′_(a△)(G)≤max{9,△(G)+1}.

关 键 词：弱邻点可区别边染色 圈 平面图 最大度 

分 类 号：O157.5[理学—数学]