The Injective Chromatic Index of a Claw-Free Subcubic Graph is at Most 6  

作　　者：Xiaoyuan DONG Yuquan LIN Wensong LIN 

机构地区：[1]Department of Primary Education,Nantong Normal College,Jiangsu 226000,P.R.China [2]School of Mathematics,Southeast University,Jiangsu 210096,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第4期409-416,共8页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11771080).

摘　　要：A coloring of edges of a graph G is injective if for any two distinct edges e1 and e2,the coloring of e1 and e2 are distinct if they are at distance 2 in G or in a common 3-cycle.The injective chromatic index of G is the minimum number of colors needed for an injective edge coloring of G.It was conjectured that the injective chromatic index of any subcubic graph is at most 6.In this paper,we partially confirm this conjecture by showing that the injective chromatic index of any claw-free subcubic graph is less than or equal to 6.The bound 6 is tight and our proof implies a linear-time algorithm for finding an injective edge coloring using at most 6 colors for such graphs.

关 键 词：injective edge coloring injective chromatic index CLAW-FREE subcubic graph 

分 类 号：O157.5[理学—数学]