Hamiltonian Cycles in Almost Claw-Free Graphs
✍ Scribed by MingChu Li
- Publisher
- Springer Japan
- Year
- 2001
- Tongue
- English
- Weight
- 209 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract In this paper, we show that every 3‐connected claw‐free graph on n vertices with δ ≥ (__n__ + 5)/5 is hamiltonian. © 1993 John Wiley & Sons, Inc.
## Abstract M. Matthews and D. Sumner have proved that of __G__ is a 2‐connected claw‐free graph of order __n__ such that δ ≧ (__n__ − 2)/3, then __G__ is hamiltonian. We prove that the bound for the minimum degree δ can be reduced to __n__/4 under the additional condition that __G__ is not in __F_
## Abstract We say that __G__ is almost claw‐free if the vertices that are centers of induced claws (__K__~1,3~) in __G__ are independent and their neighborhoods are 2‐dominated. Clearly, every claw‐free graph is almost claw‐free. It is shown that (i) every even connected almost claw‐free graph has
We show that every 3-connected claw-free graphs having at most 5S-10 vertices is hamiltonian, where 6 is the minimum degree. For regular 3-connected claw-free graphs, a related result was obtained by Li and Liu (preprint), but for nonregular claw-free graphs the best-known result comes from the work