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Graph Isomorphism for Graph Classes Characterized by Two Forbidden Induced Subgraphs

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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

We study the complexity of the Graph Isomorphism problem on graph classes that are characterized by a finite number of forbidden induced subgraphs, focusing mostly on the case of two forbidden subgraphs. We show hardness results and develop techniques for the structural analysis of such graph classes, which applied to the case of two forbidden subgraphs give the following results: A dichotomy into isomorphism complete and polynomial-time solvable graph classes for all but finitely many cases, whenever neither of the forbidden graphs is a clique, a pan, or a complement of these graphs. Further reducing the remaining open cases we show that (with respect to graph isomorphism) forbidding a pan is equivalent to forbidding a clique of size three.

In this version some proofs are omitted. For these the reader is referred to [12].

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Author information

Authors and Affiliations

  1. Utrecht University, The Netherlands

    Stefan Kratsch

  2. The Australian National University, Australia

    Pascal Schweitzer

Authors
  1. Stefan Kratsch
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  2. Pascal Schweitzer
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Editor information

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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Kratsch, S., Schweitzer, P. (2012). Graph Isomorphism for Graph Classes Characterized by Two Forbidden Induced Subgraphs. 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_7

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  • DOI: https://doi.org/10.1007/978-3-642-34611-8_7

  • 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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