HongJian Lai ; Yehong Shao ; Ju Zhou ; Hehui Wu

Every $3$connected, essentially $11$connected line graph is hamiltonian
dmtcs:3452 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

https://doi.org/10.46298/dmtcs.3452
Every $3$connected, essentially $11$connected line graph is hamiltonian
Authors: HongJian Lai ^{1}; Yehong Shao ^{1}; Ju Zhou ^{1}; Hehui Wu ^{1}
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HongJian Lai;Yehong Shao;Ju Zhou;Hehui Wu
1 Department of Mathematics [Morgantown]
Thomassen conjectured that every $4$connected line graph is hamiltonian. A vertex cut $X$ of $G$ is essential if $GX$ 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 that every $3$connected, essentially $11$connected clawfree graph is hamiltonian.