an:07314972
Zbl 07314972
Zhang, Dong Han; Lu, You; Zhang, Sheng Gui
Neighbor sum distinguishing total choice number of planar graphs without 6-cycles
EN
Acta Math. Sin., Engl. Ser. 36, No. 12, 1417-1428 (2020).
00459256
2020
j
05C15 05C10
planar graphs; neighbor sum distinguishing total choice number; combinatorial nullstellensatz
Summary: \textit{M. Pil??niak} and \textit{M. Wo??niak} [Graphs Comb. 31, No. 3, 771--782 (2015; Zbl 1312.05054)] put forward the concept of neighbor sum distinguishing (NSD) total coloring and conjectured that any graph with maximum degree \(\Delta\) admits an NSD total \((\Delta+3)\)-coloring. \textit{C. Qu} et al. [J. Comb. Optim. 32, No. 3, 906--916 (2016; Zbl 1348.05082)] showed that the list version of the conjecture holds for any planar graph with \(\Delta\geq 13\). In this paper, we prove that any planar graph with \(\Delta\geq 7\) but without 6-cycles satisfies the list version of the conjecture.
Zbl 1312.05054; Zbl 1348.05082