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.
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)。
