Szczegóły publikacji
Opis bibliograficzny
On minimum ${K_{q},k}$ stable graphs / J. L. Fouquet, H. Thuillier, J. M. Vanherpe, A. P. WOJDA // Discussiones Mathematicae. Graph Theory ; ISSN 1234-3099. — 2013 — vol. 33 iss. 1, s. 101–115. — Bibliogr. s. 114–115, Abstr. — W bazie Web of Science pominięte nazwisko A. P. Wojdy
Autorzy (4)
- Fouquet Jean-Luc
- Thuillier Henri
- Vanherpe J. M.
- AGHWojda Adam Paweł
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 71793 |
|---|---|
| Data dodania do BaDAP | 2013-02-28 |
| Tekst źródłowy | URL |
| DOI | 10.7151/dmgt.1656 |
| Rok publikacji | 2013 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discussiones Mathematicae, Graph Theory |
Abstract
A graph G is a (K-q, k) stable graph (q >= 3) if it contains a K-q after deleting any subset of k vertices (k >= 0). Andrzej Zak in the paper On (K-q; k)-stable graphs, (doi:/10.1002/jgt.21705) has proved a conjecture of Dudek, Szymanski and Zwonek stating that for sufficiently large k the number of edges of a minimum (K-q, k) stable graph is (2q - 3)(k + 1) and that such a graph is isomorphic to sK(2q-2) + tK(2q-3) where s and t are integers such that s(q - 1) + t(q - 2) - 1 = k. We have proved (Fouquet et al. On (K-q, k) stable graphs with small k, Elektron. J. Combin. 19 (2012) #P50) that for q >= 5 and k <= q/2 + 1 the graph Kq+k is the unique minimum (K-q, k) stable graph. In the present paper we are interested in the (K-q, k(q)) stable graphs of minimum size where k(q) is the maximum value for which for every nonnegative integer k < k(q) the only (K-q, k) stable graph of minimum size is Kq+k and by determining the exact value of k(q).
