摘要
Pilsniak and Wozniak put forward the concept of neighbor sum distinguishing(NSD)total coloring and conjectured that any graph with maximum degreeΔadmits an NSD total(Δ+3)-coloring in 2015.In 2016,Qu et al.showed that the list version of the conjecture holds for any planar graph withΔ≥13.In this paper,we prove that any planar graph withΔ≥7 but without 6-cycles satisfies the list version of the conjecture.
基金
Supported by National Natural Science Foundation of China(Grant Nos.11871397,11671320 and U1803263)
the Fundamental Research Funds for the Central Universities(Grant No.3102019ghjd003)
the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2020JM-083)
Shangluo University Key Disciplines Project(Discipline name Mathematics)。
