不含4-,5-圈且无相交3-面的平面图的星边染色  

Star Edge-coloring of Plane Graphs Without 4-,5-Cycles and Intersecting 3-Faces

作　　者：谢金苹 徐常青[1] Xie Jinping;Xu Changqing(School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《南开大学学报（自然科学版）》2020年第4期8-14,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(11671232)。

摘　　要：图G的星边染色是指G的一个正常边染色满足G中无长为4的路(或圈)是2-边染色的.使得图G有星边染色的最小颜色数k称为G的星边色数,记为χ′st(G).证明了若平面图G不含4-5-圈且无相交3-面,则χ′st(G)≤[1.5Δ]+10.A star edge-coloring of a graph G is a proper edge coloring without 2-colored paths(or cycles)of length 4.The smallest k for which G admits a star edge-coloring with k colors is called the star chromatic index,denoted byχ′st(G).In this paper,it is proved that if G is a plane graph without 4-,5-cycles and intersecting 3-faces,thenχ′st(G)≤[1.5Δ]+10.

关 键 词：平面图 星边染色 星边色数 

分 类 号：O157.5[理学—数学]