Hong-Jian 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 hamiltonianConference paper

Authors: Hong-Jian Lai 1; Yehong Shao 1; Ju Zhou 1; Hehui Wu 1

  • 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 claw-free graph is hamiltonian.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: Line graph,claw-free graph,supereulerian graphs,collapsible graph,hamiltonian graph,dominating Eulerian subgraph,essential connectivity,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

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