Every $3$-connected, essentially $11$-connected line graph is hamiltonian

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 nontrivial components. We prove that every $3$-connected, essentially $11$-connected line graph is hamiltonian. Using Ryjáček's line graph closure, it follows...

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Bibliographic Details
Main Authors: Hong-Jian Lai, Yehong Shao, Ju Zhou, Hehui Wu
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2005-01-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
essential connectivity
line graph
claw-free graph
supereulerian graphs
collapsible graph
hamiltonian graph
dominating eulerian subgraph
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[math.math-co] mathematics [math]/combinatorics [math.co]
Online Access:https://dmtcs.episciences.org/3452/pdf

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https://dmtcs.episciences.org/3452/pdf

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