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 language | English |
---|---|
Pages (from-to) | 211-224 |
Number of pages | 14 |
Journal | Acta Mathematicae Applicatae Sinica |
Volume | 40 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2024 |
Keywords
- 05C15
- combinatorial nullstellensatz
- discharging method
- neighbor sum distinguishing total choosibility
- planar graphs