Czechoslovak Mathematical Journal, Vol. 72, No. 1, pp. 111-124, 2022
Neighbor sum distinguishing list total coloring of IC-planar graphs without 5-cycles
Donghan Zhang
Received August 4, 2020. Published online November 15, 2021.
Abstract: Let $G=(V(G),E(G))$ be a simple graph and $E_G(v)$ denote the set of edges incident with a vertex $v$. A neighbor sum distinguishing (NSD) total coloring $\phi$ of $G$ is a proper total coloring of $G$ such that $\sum_{z\in E_G(u)\cup\{u\}}\phi(z)\neq\sum_{z\in E_G(v)\cup\{v\}}\phi(z)$ for each edge $uv\in E(G)$. Pilśniak and Woźniak asserted in 2015 that each graph with maximum degree $\Delta$ admits an NSD total $(\Delta+3)$-coloring. We prove that the list version of this conjecture holds for any IC-planar graph with $\Delta\geq11$ but without $5$-cycles by applying the Combinatorial Nullstellensatz.
Keywords: IC-planar graph; neighbor sum distinguishing list total coloring; Combinatorial Nullstellensatz; discharging method
Affiliations: Donghan Zhang, School of Mathematics and Statistics, Northwestern Polytechnical University, 1 Dongxiang Road, Chang'an District, Xi'an, Shaanxi 710129, P. R. China and School of Mathematics and Computer Application, Shangluo University, Shangluo, Shaanxi 726000, P. R. China, e-mail: zhang_dh@mail.nwpu.edu.cn
