A well-known conjecture of Thomassen says that every 4-connected line graph is hamiltonian. In this paper we prove that every 7-connected line graph is hamiltonian-connected. For line graph, C. Thomassen [l] made the following conjecture. Conjecture. Every 4-connected line graph is hamiltonian.
On the genus and connectivity of Hamiltonian graphs
β Scribed by Richard A. Duke
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 675 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0012-365X
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Thomassen conjectured that every 4-connected line graph is hamiltonian. Here we shall see that 4-connected line graphs of claw free graphs are hamiltonian connected.