Entire choosability of near-outerplane graphs

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Abstract

It is proved that if G is a plane embedding of a K4-minor-free graph with maximum degree Δ, then G is entirely 7-choosable if Δ ≤ 4 and G is entirely (Δ + 2)-choosable if Δ ≥ 5; that is, if every vertex, edge and face of G is given a list of max {7, Δ + 2} colours, then every element can be given a colour from its list such that no two adjacent or incident elements are given the same colour. It is proved also that this result holds if G is a plane embedding of a K2, 3-minor-free graph or a (over(K2, ̄) + (K1 ∪ K2))-minor-free graph. As a special case this proves that the Entire Coluring Conjecture, that a plane graph is entirely (Δ + 4)-colourable, holds if G is a plane embedding of a K4-minor-free graph, a K2, 3-minor-free graph or a (over(K2, ̄) + (K1 ∪ K2))-minor-free graph. © 2008 Elsevier B.V. All rights reserved.

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APA

Hetherington, T. J. (2009). Entire choosability of near-outerplane graphs. Discrete Mathematics, 309(8), 2153–2165. https://doi.org/10.1016/j.disc.2008.04.043

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