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
Mengerian properties, hamiltonicity, and claw-free graphs
โ Scribed by E. Flandrin; H. Li
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 603 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Using Ryja c ek's closure, we prove that any 3-connected claw-free graph of order & and minimum degree $ &+38 10 is hamiltonian. This improves a theorem of Kuipers and Veldman who got the same result with the stronger hypotheses $ &+29 8 and & sufficiently large and nearly proves their conjecture sa
## Abstract Let __G__ be a graph and let __V__~0~โ=โ{ฮฝโ __V__(__G__): __d__~__G__~(ฮฝ)โ=โ6}. We show in this paper that: (i) if __G__ is a 6โconnected line graph and if |__V__~0~|โโคโ29 or __G__[__V__~0~] contains at most 5 vertex disjoint __K__~4~'s, then __G__ is Hamiltonโconnected; (ii) every 8โco
## Abstract Let __cl__(__G__) denote Ryjรกฤek's closure of a clawโfree graph __G__. In this article, we prove the following result. Let __G__ be a 4โconnected clawโfree graph. Assume that __G__[__N__~__G__~(__T__)] is cyclically 3โconnected if __T__ is a maximal __K__~3~ in __G__ which is also maxim