Injective △+2 Coloring of Planar Graph Without Short Cycles  

作　　者：Ying CHEN Lan TAO Li ZHANG 

机构地区：[1]School of Mathematical Sciences,Tongji University,Shanghai 200092,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第4期1009-1031,共23页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (No.11871377)。

摘　　要：A coloring of graph G is an injective coloring if its restriction to the neighborhood of any vertex is injective, which means that any two vertices get different colors if they have a common neighbor. The injective chromatic number χi(G) of G is the least integer k such that G has an injective k-coloring. In this paper, we prove that(1) if G is a planar graph with girth g ≥ 6 and maximum degree △ ≥ 7, then χi(G) ≤ △ + 2;(2) if G is a planar graph with △ ≥ 24 and without 3,4,7-cycles, then χi(G) ≤ △ + 2.

关 键 词：injective coloring planar graph maximum degree CYCLE 

分 类 号：O157.5[理学—数学]