Abstract
Pilsniak and Woźniak put forward the concept of neighbor sum distinguishing (NSD) total coloring and conjectured that any graph with maximum degree Δ admits an NSD total (Δ + 3)-coloring in 2015. In 2016, Qu et al. showed that the list version of the conjecture holds for any planar graph with Δ ≥ 13. In this paper, we prove that any planar graph with Δ Δ 7 but without 6-cycles satisfies the list version of the conjecture.
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We are grateful to all anonymous referees for their time and constructive comments.
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Supported by National Natural Science Foundation of China (Grant Nos. 11871397, 11671320 and U1803263), the Fundamental Research Funds for the Central Universities (Grant No. 3102019ghjd003), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2020JM-083) and Shangluo University Key Disciplines Project (Discipline name: Mathematics) 1) Corresponding author
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Zhang, D.H., Lu, Y. & Zhang, S.G. Neighbor Sum Distinguishing Total Choice Number of Planar Graphs without 6-cycles. Acta. Math. Sin.-English Ser. 36, 1417–1428 (2020). https://doi.org/10.1007/s10114-020-0144-1
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DOI: https://doi.org/10.1007/s10114-020-0144-1