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Triangulation and Clique Separator Decomposition of Claw-Free Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7551))

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Abstract

Finding minimal triangulations of graphs is a well-studied problem with many applications, for instance as first step for efficiently computing graph decompositions in terms of clique separators. Computing a minimal triangulation can be done in O(nm) time and much effort has been invested to improve this time bound for general and special graphs. We propose a recursive algorithm which works for general graphs and runs in linear time if the input is a claw-free graph and the length of its longest path is bounded by a fixed value k. More precisely, our algorithm runs in O(f + km) time if the input is a claw-free graph, where f is the number of fill edges added, and k is the height of the execution tree; we find all the clique minimal separators of the input graph at the same time. Our algorithm can be modified to a robust algorithm which runs within the same time bound: given a non-claw free input, it either triangulates the graph or reports a claw.

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Authors and Affiliations

  1. LIMOS UMR CNRS 6158, Ensemble Scientifique des Cézeaux, Université Blaise Pascal, 63 173, Aubière, France

    Anne Berry & Annegret Wagler

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  1. Anne Berry
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  2. Annegret Wagler
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Editors and Affiliations

  1. Department of Computer Science, Caesarea Rothschild Institute (CRI), 31905, Haifa, Israel

    Martin Charles Golumbic

  2. The Academic College of Tel Aviv, Unit of Statistics and Probability Studies, 64044, Yaffo, Israel

    Michal Stern

  3. Shenkar College and Caesarea Rothschild Institute (CRI), University of Haifa, 31905, Haifa, Israel

    Avivit Levy

  4. Caesarea Rothschild Institute (CRI), 31905, Haifa, Israel

    Gila Morgenstern

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Berry, A., Wagler, A. (2012). Triangulation and Clique Separator Decomposition of Claw-Free Graphs. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-34611-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34610-1

  • Online ISBN: 978-3-642-34611-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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