On probe co-bipartite and probe diamond-free graphs
Flavia Bonomo, Celina M.H. de Figueiredo, Guillermo Durán, Luciano N. Grippo, Martín D. Safe, Jayme Luiz SZWARCFITER · Discrete Mathematics & Theoretical Computer Science · 2015
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.