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Research articles

ScienceAsia 49 (2023):ID 584-587 |doi: 10.2306/scienceasia1513-1874.2023.022


Neighbor sum distinguishing total choosability of triangle-free IC-planar graphs


Fugang Chao, Chao Li*, Donghan Zhang

 
ABSTRACT:      A proper total coloring ? of G with P z?EG(u)?{u} ?(z) 6= P z?EG(v)?{v} ?(z) for each uv ? E(G) is called a neighbor sum distinguishing (NSD) total coloring. Pil?sniak and Wo?zniak conjectured that every graph with maximum degree ? exists an NSD total (?+3)-coloring. In this paper, we improve the results of Song et al [Acta Math Sin (Engl Ser) 36(2020):292?304] to the list version by applying the combinatorial nullstellensatz.

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a School of Mathematics and Computer Application, Shangluo University, Shangluo 726000 China

* Corresponding author, E-mail: lichao_math@163.com

Received 21 Feb 2022, Accepted 13 Jan 2023