The entire choosability of plane graphs

Weifan Wang (), Tingting Wu, Xiaoxue Hu and Yiqiao Wang
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Weifan Wang: Zhejiang Normal University
Tingting Wu: Zhejiang Normal University
Xiaoxue Hu: Zhejiang Normal University
Yiqiao Wang: Beijing University of Chinese Medicine

Journal of Combinatorial Optimization, 2016, vol. 31, issue 3, No 18, 1240 pages

Abstract: Abstract A plane graph $$G$$ G is entirely $$k$$ k -choosable if, for every list $$L$$ L of colors satisfying $$L(x)=k$$ L ( x ) = k for all $$x\in V(G)\cup E(G) \cup F(G)$$ x ∈ V ( G ) ∪ E ( G ) ∪ F ( G ) , there exists a coloring which assigns to each vertex, each edge and each face a color from its list so that any adjacent or incident elements receive different colors. In 1993, Borodin proved that every plane graph $$G$$ G with maximum degree $$\Delta \ge 12$$ Δ ≥ 12 is entirely $$(\Delta +2)$$ ( Δ + 2 ) -choosable. In this paper, we improve this result by replacing 12 by 10.

Keywords: Plane graph; Entire choosability; Maximum degree (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9819-9

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