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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Contributor : Nicolas Trotignon <>
Submitted on : Thursday, November 19, 2015 - 8:35:59 AM
Last modification on : Thursday, February 7, 2019 - 2:52:29 PM

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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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