Szczegóły publikacji
Opis bibliograficzny
A generalization of Dirac's theorem on cycles through $k$ vertices in $k$-connected graphs / Evelyne Flandrin, Hao Li, Antoni MARCZYK, Mariusz WOŹNIAK // Discrete Mathematics ; ISSN 0012-365X. — 2007 — vol. 307 iss. 7–8 spec. iss., s. 878–884. — Bibliogr. s. 883–884, Abstr. — Publikacja dostępna online od: 2006-09-26. — 12th Cycles and colourings 2003 Workshop : Stara Lesna, Slovakia, August 31–September 05, 2003
Autorzy (4)
- Flandrin Evelyne
- Li Hao
- AGHMarczyk Antoni
- AGHWoźniak Mariusz
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 36419 |
|---|---|
| Data dodania do BaDAP | 2008-01-19 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.disc.2005.11.052 |
| Rok publikacji | 2007 |
| Typ publikacji | referat w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete Mathematics |
Abstract
Let X be a subset of the vertex set of a graph G. We denote by K(X) the smallest number of vertices separating two vertices of X if X does not induce a complete subgraph of G, otherwise we put kappa(X) = vertical bar X vertical bar - 1 if vertical bar X vertical bar >= 2 and K(X) = 1 if vertical bar X vertical bar = 1. We prove that if kappa(X) >= 2 then every set of at most kappa(X) vertices of X is contained in a cycle of G. Thus, we generalize a similar result of Dirac. Applying this theorem we improve our previous result involving an Ore-type condition and give another proof of a slightly improved version of a theorem of Broersma et al. (c) 2006 Elsevier B.V. All rights reserved.
