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arXiv · 1309.7120

Wheel-free planar graphs

Pierre Aboulker·Maria Chudnovsky·Paul Seymour·Nicolas Trotignon
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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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Pierre Aboulker, Maria Chudnovsky, Paul Seymour, Nicolas Trotignon. 2014-08-18. Wheel-free planar graphs. https://doi.org/10.1016/j.ejc.2015.02.027

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