On probe 2-clique graphs and probe diamond-free graphs

BONOMO, FLAVIA; DE FIGUEIREDO, CELINA; DURÁN, GUILLERMO; GRIPPO, LUCIANO NORBERTO; SAFE, MARTÍN DARÍO; SZWARCFITER, JAYME

DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE (DMTCS)

DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE

Lugar: Nancy; Año: 2015 vol. 17 p. 187 - 200

1365-8050

Given a class G of graphs, probe G graphs are defined as follows. A graph H is probe G if there exists a partition of its vertices into a set of probe vertices and a stable set of nonprobe vertices in such a way that non-edges of H, whose endpoints are nonprobe vertices, can be added so that the resulting graph belongs to G. We investigate probe 2-clique graphs and probe diamond-free graphs. For probe 2-clique graphs, we present a polynomial-time recognition algorithm. Probe diamond-free graphs are characterized by minimal forbidden induced subgraphs. As a by-product, it is proved that the class of probe block graphs is the intersection between the classes of chordal graphs and probe diamond-free graphs.