Neighbor Sum Distinguishing Total Choice Number of Planar Graphs without 6-cycles

• 作者: Dong Han ZHANG Sheng Gui ZHANG You LU
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2020,（12）
• 页码范围: 1417-1428
• 页数: 12页
• 语种: 英文

摘要

Pil?niak and Wo?niak put forward the concept of neighbor sum distinguishing (NSD) total coloring and conjectured that any graph with maximum degree Δadmits 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 with Δ≥ 13. In this paper, we prove that any planar graph with Δ≥ 7 but without 6-cycles satisfies the list version of the conjecture.