Wheel-free planar graphs

Pierre Aboulker; Maria Chudnovsky; Paul Seymour; Nicolas Trotignon

doi:10.1016/j.ejc.2015.02.027

Wheel-free planar graphs

Pierre Aboulker, Maria Chudnovsky, Paul Seymour, Nicolas Trotignon

Mathematics

Research output: Contribution to journal › Article

2 Scopus citations

Abstract

A 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.

Original language	English (US)
Pages (from-to)	57-67
Number of pages	11
Journal	European Journal of Combinatorics
Volume	49
DOIs	https://doi.org/10.1016/j.ejc.2015.02.027
State	Published - Oct 1 2015

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2015.02.027

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Aboulker, P., Chudnovsky, M., Seymour, P., & Trotignon, N. (2015). Wheel-free planar graphs. European Journal of Combinatorics, 49, 57-67. https://doi.org/10.1016/j.ejc.2015.02.027

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