Neighbor sum distinguishing total choice number of NIC-planar graphs with restricted conditions. (18th August 2021) - Zhang, Donghan
Abstract: A NIC-planar graph is a graph that has a drawing in the plane such that each edge is crossed at most once and any two pairs of crossing edges share at most one common vertex. Let EG ( u ) denote the set of edges incident with a vertex u . A neighbor sum distinguishing (NSD) total coloring ϕ of G is a proper total coloring of G such that for each edge uυ ∈ E ( G ) . Pilśniak and Woźniak conjectured that any graph with maximum degree Δ admits an NSD total (Δ+ 3) -coloring. In this paper, we prove that the list version of the conjecture holds for any triangle-free NIC-planar graph with Δ ≥ 8 and with each vertex incident with at most two crossing edges by applying the Combinatorial Nullstellensatz.