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The entire choosability of plane graphs

Author

Listed:
  • Weifan Wang

    (Zhejiang Normal University)

  • Tingting Wu

    (Zhejiang Normal University)

  • Xiaoxue Hu

    (Zhejiang Normal University)

  • Yiqiao Wang

    (Beijing University of Chinese Medicine)

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.

Suggested Citation

  • Weifan Wang & Tingting Wu & Xiaoxue Hu & Yiqiao Wang, 2016. "The entire choosability of plane graphs," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1221-1240, April.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:3:d:10.1007_s10878-014-9819-9
    DOI: 10.1007/s10878-014-9819-9
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