On $({K}\_{q},k)$ stable graphs with small $k$

Jean-Luc Fouquet (1) , Henri Thuillier (1) , Jean-Marie Vanherpe (1) , Adam Pawel Wojda (2)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans
2 AGH UST - AGH University of Science and Technology [Krakow, PL]

A graph G is (Kq; k) stable if it contains a copy of Kq after deleting any subset of k vertices. In a previous paper we have characterized the (Kq; k) stable graphs with minimum size for 2 < q < 6 and we have proved that the only (Kq; k) stable graph with minimum size is Kq+k for q > 4 and k < 4. We show that for q > 5 and k <= q/2+1 the only (Kq; k) stable graph with minimum size is isomorphic to Kq+k.

Mots clés: stable graphs

Domaines: Mathématique discrète [cs.DM]

Jean-Luc Fouquet, Henri Thuillier, Jean-Marie Vanherpe, Adam Pawel Wojda. On $({K}\_{q},k)$ stable graphs with small $k$. The Electronic Journal of Combinatorics, 2012, 19 (2), pp.#P50. ⟨hal-00934318⟩