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Linear-time certifying recognition for partitioned probe cographs

Authors: Van Bang Le and H.N. de Ridder

Published in: Dagstuhl Seminar Proceedings, Volume 7211, Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes (2007)

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.

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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)

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@InProceedings{le_et_al:DagSemProc.07211.2,
  author =	{Le, Van Bang and de Ridder, H.N.},
  title =	{{Linear-time certifying recognition for partitioned probe cographs}},
  booktitle =	{Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7211},
  editor =	{Andreas Brandst\"{a}dt and Klaus Jansen and Dieter Kratsch and Jeremy P. Spinrad},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07211.2},
  URN =		{urn:nbn:de:0030-drops-12703},
  doi =		{10.4230/DagSemProc.07211.2},
  annote =	{Keywords: Cograph, probe cograph, certifying graph algorithm}
}

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Documents authored by de Ridder, H.N.

Linear-time certifying recognition for partitioned probe cographs

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