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

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.
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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (in progress) (1), pp.187--199
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Flavia Bonomo, Celina M. H. Figueiredo, Guillermo Duran, Luciano N. Grippo, Martín D. Safe, et al.. On probe 2-clique graphs and probe diamond-free graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (in progress) (1), pp.187--199. 〈hal-01196866〉

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