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Neighbor sum distinguishing total choice number of planar graphs without 6-cycles. (English) Zbl 07314972
Summary: M. Pilśniak and M. Woźniak [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. 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.
MSC:
05C15 Coloring of graphs and hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
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