Every longest circuit of a 3-connected, \(K_{3,3}\)-minor free graph has a chord

Every longest circuit of a 3-connected, \(K_{3,3}\)-minor free graph has a chord

Carsten Thomassen conjectured that every longest circuit in a 3-connected graph has a chord. We prove the conjecture for graphs having no \(K_{3,3}\) minor, and consequently for planar graphs.

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Veröffentlicht in:arXiv.org 2008-03
1. Verfasser: Birmelé, E
Format: Artikel
Sprache:eng
Schlagworte:
Circuits
Graphs
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Beschreibung
Zusammenfassung:Carsten Thomassen conjectured that every longest circuit in a 3-connected graph has a chord. We prove the conjecture for graphs having no \(K_{3,3}\) minor, and consequently for planar graphs.
ISSN:2331-8422
DOI:10.48550/arxiv.0711.2360