## Abstract We show that every 3‐connected claw‐free graph which contains no induced copy of __P__~11~ is hamiltonian. Since there exist non‐hamiltonian 3‐connected claw‐free graphs without induced copies of __P__~12~ this result is, in a way, best possible. © 2004 Wiley Periodicals, Inc. J Graph T
All 4-connected Line Graphs of Claw Free Graphs Are Hamiltonian Connected
✍ Scribed by Matthias Kriesell
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 109 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0095-8956
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✦ Synopsis
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.
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