Acyclic 6-choosability of Planar Graphs without 5-cycles and Adjacent 4-cycles  

作　　者：Lin SUN 

机构地区：[1]School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524000,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第6期992-1004,共13页数学学报（英文版）

基　　金：Supported by Guangdong Province Basic and Applied Basic Research Foundation and Joint Foundation Project(Grant No.2019A1515110324);Natural Science Foundation of Guangdong province(Grant No.2019A1515011031);University Characteristic Innovation Project of Guangdong province(Grant No.2019KTSCX092)。

摘　　要：A proper vertex coloring of a graph is acyclic if every cycle uses at least three colors.A graph G is acyclically k-choosable if for any list assignment L={L(v):v∈V(G)}with|L(v)|≥k for all v∈V(G),there exists a proper acyclic vertex coloringφof G such thatφ(v)∈L(v)for all v∈V(G).In this paper,we prove that if G is a planar graph and contains no 5-cycles and no adjacent 4-cycles,then G is acyclically 6-choosable.

关 键 词：Planar graph acyclic coloring acyclic choosability 

分 类 号：O157.5[理学—数学]