2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 379382
author:  HongJian Lai, Yehong Shao, Ju Zhou and Hehui Wu 

title:  Every 3connected, essentially 11connected line graph is hamiltonian 
keywords:  Line graph, clawfree 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
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.

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reference:  HongJian Lai and Yehong Shao and Ju Zhou and Hehui Wu (2005), Every 3connected, essentially 11connected 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. 379382 
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