Wheel-free planar graphs

Abstract : A \emph{wheel} is a graph formed by a chordless cycle $C$ and a vertex $u$ not in $C$ that has at least three neighbors in $C$. We prove that every 3-connected planar graph that does not contain a wheel as an induced subgraph is either a line graph or has a clique cutset. We prove that every planar graph that does not contain a wheel as an induced subgraph is 3-colorable.
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European Journal of Combinatorics, Elsevier, 2015, 49, <10.1016/j.ejc.2015.02.027>
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https://hal.archives-ouvertes.fr/hal-01230782
Contributeur : Nicolas Trotignon <>
Soumis le : jeudi 19 novembre 2015 - 08:35:59
Dernière modification le : mardi 11 octobre 2016 - 14:06:43

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Pierre Aboulker, Maria Chudnovsky, Paul Seymour, Nicolas Trotignon. Wheel-free planar graphs. European Journal of Combinatorics, Elsevier, 2015, 49, <10.1016/j.ejc.2015.02.027>. <hal-01230782>

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