Discrete Mathematics & Theoretical Computer Science, Vol 17, No 1 (2015)

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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


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.

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