Neighbor Sum Distinguishing Total Choosability of Planar Graphs with Maximum Degree at Least 10

Dong han Zhang, You Lu, Sheng gui Zhang, Li Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

A neighbor sum distinguishing (NSD) total coloring ϕ of G is a proper total coloring of G such that ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each edge uv ∈ E(G), where EG(u) is the set of edges incident with a vertex u. In 2015, Pilśniak and Woźniak conjectured that every graph with maximum degree Δ has an NSD total (Δ + 3)-coloring. Recently, Yang et al. proved that the conjecture holds for planar graphs with Δ ≥ 10, and Qu et al. proved that the list version of the conjecture also holds for planar graphs with Δ ≥ 13. In this paper, we improve their results and prove that the list version of the conjecture holds for planar graphs with Δ ≥ 10.

Original languageEnglish
Pages (from-to)211-224
Number of pages14
JournalActa Mathematicae Applicatae Sinica
Volume40
Issue number1
DOIs
StatePublished - Jan 2024

Keywords

  • 05C15
  • combinatorial nullstellensatz
  • discharging method
  • neighbor sum distinguishing total choosibility
  • planar graphs

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