Canonical Representations for Circular-Arc Graphs Using Flip Sets

Abstract

We show that computing canonical representations for circular-arc (CA) graphs reduces to computing certain subsets of vertices called flip sets. For a broad class of CA graphs, which we call uniform, it suffices to compute a CA representation to find such flip sets. As a consequence canonical representations for uniform CA graphs can be obtained in polynomial-time. We then investigate what kind of CA graphs pose a challenge to this approach. This leads us to introduce the notion of restricted CA matrices and show that the canonical representation problem for CA graphs is logspace-reducible to that of restricted CA matrices. As a byproduct, we obtain the result that CA graphs without induced 4-cycles can be canonized in logspace.

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Acknowledgements

We thank the anonymous reviewers for their insightful comments and suggestions that helped us to improve the quality of this work.

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Correspondence to Maurice Chandoo.

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Chandoo, M. Canonical Representations for Circular-Arc Graphs Using Flip Sets. Algorithmica 80, 3646–3672 (2018). https://doi.org/10.1007/s00453-018-0410-0

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Keywords

  • Canonization
  • Circular-arc graphs
  • Isomorphism

Mathematics Subject Classification

  • G.2.2 Graph Theory