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

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 res...

Full description

Bibliographic Details
Authors: Bonomo, Flavia, Figueiredo, Celina M. H. de, Duran, Guillermo Alfredo, Grippo, Luciano Norberto, Safe, Martin Dario, Szwarcfiter, Jayme L.
Format: article
Status:Published version
Publication Date:2015
Country:Argentina
Institution:Consejo Nacional de Investigaciones Científicas y Técnicas
Repository:CONICET Digital (CONICET)
Language:English
OAI Identifier:oai:ri.conicet.gov.ar:11336/21313
Online Access:http://hdl.handle.net/11336/21313
Access Level:Open access
Keyword:2-Clique Graphs
Diamond-Free Graphs
Probe Graphs
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.2
Description
Summary: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.

Similar Items