Longest Cycles in Almost Claw-Free Graphs
β Scribed by MingChu Li
- Publisher
- Springer Japan
- Year
- 2000
- Tongue
- English
- Weight
- 192 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
In this paper, we show that every 2-connected, k-regular claw-free graph on n vertices contains a cycle of length at least min {4k-2, n} (k >~ 8), and this result is best possible. ## I. Introduction All graphs considered here are undirected and finite, without loops or multiple edges. A graph G is
## Abstract We say that __G__ is almost clawβfree if the vertices that are centers of induced claws (__K__~1,3~) in __G__ are independent and their neighborhoods are 2βdominated. Clearly, every clawβfree graph is almost clawβfree. It is shown that (i) every even connected almost clawβfree graph has
Some known results on claw-free (Kl,3-free) graphs are generalized to the larger class of almost claw-free graphs which were introduced by RyjaEek. In particular, w e show that a 2-connected almost claw-free graph is I-tough, and that a 2-connected almost claw-free graph on n vertices is hamiltonian
In this article w e show that the standard results concerning longest paths and cycles in graphs can be improved for K,,,-free graphs. We obtain as a consequence of these results conditions for the existence of a hamiltonian path and cycle in K,,,-free graphs.