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Linear-time certifying recognition for partitioned probe cographs

Authors Van Bang Le, H.N. de Ridder



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Van Bang Le
H.N. de Ridder

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Van Bang Le and H.N. de Ridder. Linear-time certifying recognition for partitioned probe cographs. In Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes. Dagstuhl Seminar Proceedings, Volume 7211, pp. 1-4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)
https://doi.org/10.4230/DagSemProc.07211.2

Abstract

Cographs are those graphs without induced path on four vetices. A graph $G=(V, E)$ with a partition $V=Pcup N$ where $N$ is an independent set is a partitioned probe cograph if one can add new edges between certain vertices in $N$ in such a way that the graph obtained is a cograph. We characterize partitioned probe cographs in terms of five forbidden induced subgraphs. Using this characterization, we give a linear-time recognition algorithm for partitioned probe cographs. Our algorithm produces a certificate for membership that can be checked in linear time and a certificate for non-membership that can be checked in sublinear time.
Keywords
  • Cograph
  • probe cograph
  • certifying graph algorithm

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