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On wheel-free graphs

Pierre Aboulker 1 Frédéric Havet 2 Nicolas Trotignon 1
2 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : A wheel is a graph formed by a chordless cycle and a vertex that has at least three neighbors in the cycle. We prove that every 3-connected graph that does not contain a wheel as a subgraph is in fact minimally 3-connected. We prove that every graph that does not contain a wheel as a subgraph is 3-colorable.
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https://hal.inria.fr/inria-00602079
Contributor : Frederic Havet <>
Submitted on : Tuesday, June 21, 2011 - 2:44:21 PM
Last modification on : Wednesday, October 21, 2020 - 9:56:05 AM
Long-term archiving on: : Friday, November 9, 2012 - 4:46:04 PM

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  • HAL Id : inria-00602079, version 1

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Pierre Aboulker, Frédéric Havet, Nicolas Trotignon. On wheel-free graphs. [Research Report] RR-7651, INRIA. 2011. ⟨inria-00602079⟩

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