Bonomo, Flavia and Durán, Guillermo and Grippo, Luciano N. and Safe, Martın D. - Probe interval graphs and probe unit interval graphs on superclasses of cographs

dmtcs:602 - Discrete Mathematics & Theoretical Computer Science, August 21, 2013, Vol. 15 no. 2
Probe interval graphs and probe unit interval graphs on superclasses of cographs

Authors: Bonomo, Flavia and Durán, Guillermo and Grippo, Luciano N. and Safe, Martın D.

A graph is probe (unit) interval if its vertices can be partitioned into two sets: a set of probe vertices and a set of nonprobe vertices, so that the set of nonprobe vertices is a stable set and it is possible to obtain a (unit) interval graph by adding edges with both endpoints in the set of nonprobe vertices. Probe (unit) interval graphs form a superclass of (unit) interval graphs. Probe interval graphs were introduced by Zhang for an application concerning the physical mapping of DNA in the human genome project. The main results of this article are minimal forbidden induced subgraphs characterizations of probe interval and probe unit interval graphs within two superclasses of cographs: P4-tidy graphs and tree-cographs. Furthermore, we introduce the concept of graphs class with a companion which allows to describe all the minimally non-(probe G) graphs with disconnected complement for every graph class G with a companion.


Source : oai:HAL:hal-00980766v1
Volume: Vol. 15 no. 2
Section: Graph Theory
Published on: August 21, 2013
Submitted on: March 26, 2012
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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