Flavia Bonomo ; Celina M. H. Figueiredo ; Guillermo Duran ; Luciano N. Grippo ; Martín D. Safe et al.
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On probe 2-clique graphs and probe diamond-free graphs
On probe 2-clique graphs and probe diamond-free graphs
Authors: Flavia Bonomo 1,2; Celina M. H. Figueiredo 3; Guillermo Duran 2,4,5,6; Luciano N. Grippo 7; Martín D. Safe 7; Jayme L. Szwarcfiter 3,8
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Flavia Bonomo;Celina M. H. Figueiredo;Guillermo Duran;Luciano N. Grippo;Martín D. Safe;Jayme L. Szwarcfiter
1 Departamento de Computación [Buenos Aires]
2 Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
3 Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia
4 Departamento de Matemática [Buenos Aires]
5 Departamento de Ingenieria Industrial [Santiago]
6 Instituto de Cálculo [Buenos Aires]
7 Instituto de Ciencias [Los Polvorines]
8 Nucleo de Computação Eletrônica
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.