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On Restrictions of Balanced 2-Interval Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4769))

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Abstract

The class of 2-interval graphs has been introduced for modelling scheduling and allocation problems, and more recently for specific bioinformatics problems. Some of those applications imply restrictions on the 2-interval graphs, and justify the introduction of a hierarchy of subclasses of 2-interval graphs that generalize line graphs: balanced 2-interval graphs, unit 2-interval graphs, and (x,x)-interval graphs. We provide instances that show that all inclusions are strict. We extend the NP-completeness proof of recognizing 2-interval graphs to the recognition of balanced 2-interval graphs. Finally we give hints on the complexity of unit 2-interval graphs recognition, by studying relationships with other graph classes: proper circular-arc, quasi-line graphs, K 1,5-free graphs, ...

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Authors and Affiliations

  1. LIAFA - Univ. Paris VII,  

    Philippe Gambette

  2. LRI - Univ. Paris XI,  

    Stéphane Vialette

Authors
  1. Philippe Gambette
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  2. Stéphane Vialette
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Andreas Brandstädt Dieter Kratsch Haiko Müller

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Gambette, P., Vialette, S. (2007). On Restrictions of Balanced 2-Interval Graphs. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_6

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  • DOI: https://doi.org/10.1007/978-3-540-74839-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74838-0

  • Online ISBN: 978-3-540-74839-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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