On $(K_q,k)$ vertex stable with minimum size

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 a $(K_q,k)$ vertex stable if it contains a $K_q$ after deleting any subset of $k$ vertices. We give a characterization of $(K_q,k)$ vertex stable graphs with minimum size for $q=3,4,5$.

Domaines: Mathématique discrète [cs.DM]

Jean-Luc Fouquet, Henri Thuillier, Jean-Marie Vanherpe, Adam Pawel Wojda. On $(K_q,k)$ vertex stable with minimum size. Discrete Mathematics, 2012, 312 (14), pp.2109:2118. ⟨10.1016/j.disc.2011.04.017⟩. ⟨hal-00586145⟩