### On probe co-bipartite and probe diamond-free graphs

*Flavia Bonomo, Celina Miraglia Herrera de Figueiredo, Guillermo Alfredo Durán, Luciano Norberto Grippo, Martín Darío Safe, Jayme Luiz Szwarcfiter*

#### Abstract

Given a class G of graphs, probe
G graphs are defined as follows. A graph
G 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 G, 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.Full Text: PDF PostScript