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Characterizing Minimal Interval Completions

Towards Better Understanding of Profile and Pathwidth (Extended Abstract)

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STACS 2007 (STACS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4393))

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Abstract

Minimal interval completions of graphs are central in understanding two important and widely studied graph parameters: profile and pathwidth. Such understanding seems necessary to be able to attack the problem of computing these parameters. An interval completion of a given graph is an interval supergraph of it on the same vertex set, obtained by adding edges. If no subset of the added edges can be removed without destroying the interval property, we call it a minimal interval completion. In this paper, we give the first characterization of minimal interval completions. We present a polynomial time algorithm, for deciding whether a given interval completion of an arbitrary graph is minimal. If the interval completion is not minimal the algorithm can be used to extract a minimal interval completion that is a subgraph of the given interval completion.

This work is supported by the Research Council of Norway.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020 Bergen, Norway

    Pinar Heggernes & Yngve Villanger

  2. LIFO, Université d’Orleans, PB 6759, F-45067 Orleans Cedex 2, France

    Karol Suchan & Ioan Todinca

  3. Faculty of Applied Mathematics, AGH - University of Science and Technology, Krakow, Poland

    Karol Suchan

Authors
  1. Pinar Heggernes
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  2. Karol Suchan
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  3. Ioan Todinca
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  4. Yngve Villanger
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Wolfgang Thomas Pascal Weil

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Heggernes, P., Suchan, K., Todinca, I., Villanger, Y. (2007). Characterizing Minimal Interval Completions. In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_21

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  • DOI: https://doi.org/10.1007/978-3-540-70918-3_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70917-6

  • Online ISBN: 978-3-540-70918-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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