Every 3-connected essentially 10-connected line graph is Hamilton-connected

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Every 3-connected, essentially 11-connected line graph is Hamiltonian

Thomassen conjectured that every 4-connected line graph is Hamiltonian. A vertex cut X of G is essential if G−X has at least two non-trivial components. We prove that every 3-connected, essentially 11-connected line graph is Hamiltonian. Using Ryjác̆ek’s line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is Hamiltonian. © 2005 Elsevier Inc. All rights...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2012

ISSN: 0012-365X

DOI: 10.1016/j.disc.2012.08.015