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

Authors:
Hong-Jian Lai;Yehong Shao;Hehui Wu;Ju Zhou
Affiliations:
Department of Mathematics, West Virginia University, Morgantown, WV;Arts and Sciences, Ohio University Southern, Ironton, OH;Department of Mathematics, West Virginia University, Morgantown, WV;Department of Mathematics, West Virginia University, Morgantown, WV
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

Citing 3
Cited 3

On Hamiltonian line graphs and connectivity

Discrete Mathematics
On a closure concept in claw-free graphs

Journal of Combinatorial Theory Series B
Graph Theory With Applications

Graph Theory With Applications

Note: Hamiltonicity of 6-connected line graphs

Discrete Applied Mathematics
Hamilton cycles in 5-connected line graphs

European Journal of Combinatorics
Collapsible graphs and Hamiltonian connectedness of line graphs

Discrete Applied Mathematics

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Abstract

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 Ryjáček's line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is Hamiltonian.