Neighbor-distinguishing total coloring of planar graphs with maximum degree twelve

Jingjing Huo, Yiqiao Wang, Weifan Wang () and Wenjing Xia
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Jingjing Huo: Hebei University of Engineering
Yiqiao Wang: Beijing University of Chinese Medicine
Weifan Wang: Zhejiang Normal University
Wenjing Xia: Zhejiang Normal University

Journal of Combinatorial Optimization, 2020, vol. 39, issue 1, No 15, 246-272

Abstract: Abstract The neighbor-distinguishing total chromatic number $$\chi ''_{a}(G)$$χa′′(G) of a graph G is the minimum number of colors required for a proper total coloring of G such that any two adjacent vertices have different sets of colors. In this paper, we show that if G is a planar graph with $$\Delta =12$$Δ=12, then $$13\le \chi ''_{a}(G)\le 14$$13≤χa′′(G)≤14, and moreover $$\chi ''_{a}(G)=14$$χa′′(G)=14 if and only if G contains two adjacent 12-vertices.

Keywords: Planar graph; Neighbor-distinguishing total coloring; Discharging; Combinatorial Nullstellensatz; 05C15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-019-00465-3

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