In this paper, we give the following result: Let G be a 2-connected graph of order PZ> 13 and nd2az -3, where 02 = min{d(u) + d(u): uz'.$E(G)}. If the set of claw-centers of G is independent, then either G is hamiltonian or G belongs to three classes of exceptional graphs. The bound n <202 -3 is sha
Hamiltonicity of 2-connected quasi-claw-free graphs
β Scribed by Rao Li
- Book ID
- 108113412
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 215 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0012-365X
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## Abstract Let __G__ be a graph and let __V__~0~β=β{Ξ½β __V__(__G__): __d__~__G__~(Ξ½)β=β6}. We show in this paper that: (i) if __G__ is a 6βconnected line graph and if |__V__~0~|ββ€β29 or __G__[__V__~0~] contains at most 5 vertex disjoint __K__~4~'s, then __G__ is Hamiltonβconnected; (ii) every 8βco