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.