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

Hong-Jian Lai, Yehong Shao, Ju Zhou, Hehui Wu
2005 Discrete Mathematics & Theoretical Computer Science  
International audience 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 that every $3$-connected, essentially $11$-connected claw-free graph is hamiltonian.
doi:10.46298/dmtcs.3452 fatcat:am6kqfn4dvhlfgtdom2p7y6ddq