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A Necessary Condition and a Sufficient Condition for Pairwise Compatibility Graphs

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WALCOM: Algorithms and Computation (WALCOM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9627))

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Abstract

In this paper we give a necessary condition and a sufficient condition for a graph to be a pairwise compatibility graph (PCG). Let G be a graph and let \(G^c\) be the complement of G. We show that if \(G^c\) has two disjoint chordless cycles then G is not a PCG. On the other hand, if \(G^c\) has no cycle then G is a PCG. Our conditions are the first necessary condition and the first sufficient condition for pairwise compatibility graphs in general.

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References

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Acknowledgment

This work is done in the Department of Computer Science and Engineering (CSE) of Bangladesh University of Engineering and Technology (BUET). The authors gratefully acknowledge the support received from BUET.

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Authors and Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Iqbal Hossain, Sammi Abida Salma & Md. Saidur Rahman

Authors
  1. Md. Iqbal Hossain
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  2. Sammi Abida Salma
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  3. Md. Saidur Rahman
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Corresponding author

Correspondence to Md. Iqbal Hossain .

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Editors and Affiliations

  1. Dept. of Computer Science and Engin., Bangladesh Univ. of Engin. & Technol., Dhaka, Bangladesh

    Mohammad Kaykobad

  2. Dept. of Computer Science, Sapienza University of Rome, Rome, Italy

    Rossella Petreschi

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© 2016 Springer International Publishing Switzerland

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Hossain, M.I., Salma, S.A., Rahman, M.S. (2016). A Necessary Condition and a Sufficient Condition for Pairwise Compatibility Graphs. In: Kaykobad, M., Petreschi, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2016. Lecture Notes in Computer Science(), vol 9627. Springer, Cham. https://doi.org/10.1007/978-3-319-30139-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-30139-6_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30138-9

  • Online ISBN: 978-3-319-30139-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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