Neighbor Sum Distinguishing Total Choice Number of Planar Graphs without 6-cycles

Dong Han Zhang; You Lu; Sheng Gui Zhang

doi:10.1007/s10114-020-0144-1

Neighbor Sum Distinguishing Total Choice Number of Planar Graphs without 6-cycles

Dong Han Zhang
, You Lu
, Sheng Gui Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	1417-1428
Number of pages	12
Journal	Acta Mathematica Sinica, English Series
Volume	36
Issue number	12
DOIs	https://doi.org/10.1007/s10114-020-0144-1
State	Published - Dec 2020

Keywords

05C15
Combinatorial Nullstellensatz
neighbor sum distinguishing total choice number
Planar graphs

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10.1007/s10114-020-0144-1

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title = "Neighbor Sum Distinguishing Total Choice Number of Planar Graphs without 6-cycles",

abstract = "Pilsniak and Wo{\'z}niak 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.",

keywords = "05C15, Combinatorial Nullstellensatz, neighbor sum distinguishing total choice number, Planar graphs",

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AU - Lu, You

AU - Zhang, Sheng Gui

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N2 - 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.

AB - 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.

KW - 05C15

KW - Combinatorial Nullstellensatz

KW - neighbor sum distinguishing total choice number

KW - Planar graphs

UR - https://www.scopus.com/pages/publications/85097996130

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 12

ER -

Neighbor Sum Distinguishing Total Choice Number of Planar Graphs without 6-cycles

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Keywords

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