| author: | Hong-Jian Lai, Yehong Shao, Ju Zhou and Hehui Wu |
|---|---|
| title: | Every 3-connected, essentially 11-connected line graph is hamiltonian |
| keywords: | Line graph, claw-free graph, supereulerian graphs, collapsible graph, hamiltonian graph, dominating Eulerian subgraph, essential connectivity |
| 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 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.
|
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| reference: | Hong-Jian Lai and Yehong Shao and Ju Zhou and Hehui Wu (2005), Every 3-connected, essentially 11-connected line graph is hamiltonian, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 379-382 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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| pdf-source: | dmAE0173.pdf (100 K) |
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