On 4-connected claw-free well-covered graphs
✍ Scribed by Bert Hartnell; Michael D. Plummer
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 556 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0166-218X
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## Abstract We consider the existence of several different kinds of factors in 4‐connected claw‐free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4‐connected line graph is hamiltonian,
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.
A graph is Hamilton-connected if any pair of vertices is joined by a hamiltonian path. In this note it is shown that 9-connected graphs which contain no induced claw K 1, 3 are Hamilton-connected, by reformulating and localizing a closure concept due to Ryja c ek, which turns claw-free graphs into l
## Abstract We show that if __G__ is a 4‐connected claw‐free graph in which every induced hourglass subgraph __S__ contains two non‐adjacent vertices with a common neighbor outside __S__, then __G__ is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamilton