Planar graphs with $$\Delta =9$$Δ=9 are neighbor-distinguishing totally 12-colorable

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

Journal of Combinatorial Optimization, 2019, vol. 37, issue 3, No 16, 1089 pages

Abstract: Abstract The neighbor-distinguishing total coloring of a graph G is a proper total coloring of G using k colors such that any two adjacent vertices have different sets of colors. It was known that every planar graph G with $$\Delta \ge 10$$Δ≥10 is neighbor-distinguishing totally $$(\Delta +3)$$(Δ+3)-colorable. In this paper, we extend this result to the case $$\Delta =9$$Δ=9. Namely, we prove that every planar graph G with $$\Delta =9$$Δ=9 is neighbor-distinguishing totally 12-colorable.

Keywords: Planar graph; Neighbor-distinguishing total coloring; Maximum degree; Combinatorial Nullstellensatz; Discharging; 05C15 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10878-018-0334-2

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