Plane graphs with $$\Delta =7$$Δ=7 are entirely 10-colorable

Jiangxu Kong, Xiaoxue Hu () and Yiqiao Wang
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Jiangxu Kong: China Jiliang University
Xiaoxue Hu: Zhejiang University of Science and Technology
Yiqiao Wang: Beijing University of Chinese Medicine

Journal of Combinatorial Optimization, 2020, vol. 40, issue 1, No 1, 20 pages

Abstract: Abstract A plane graph G is entirely k-colorable if $$V(G)\cup E(G) \cup F(G)$$V(G)∪E(G)∪F(G) can be colored with k colors such that any two adjacent or incident elements receive different colors. In 2011, Wang and Zhu conjectured that every plane graph G with maximum degree $$\Delta \ge 3$$Δ≥3 and $$G\ne K_4$$G≠K4 is entirely $$(\Delta +3)$$(Δ+3)-colorable. It is known that the conjecture holds for the case $$\Delta \ge 8$$Δ≥8. The condition $$\Delta \ge 8$$Δ≥8 is improved to $$\Delta \ge 7$$Δ≥7 in this paper.

Keywords: Plane graph; Entire coloring; Maximum degree; 05C15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-020-00561-9

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