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Recognizing Simple-Triangle Graphs by Restricted 2-Chain Subgraph Cover

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WALCOM: Algorithms and Computation (WALCOM 2017)

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Abstract

A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was a longstanding open problem, and recently a polynomial-time algorithm has been given (SIAM J. Discrete Math. 29(3):1150–1185, 2015). Along with the approach of this paper, we show a simpler recognition algorithm for simple-triangle graphs. To do this, we provide a polynomial-time algorithm to solve the following problem: Given a bipartite graph G and a set F of edges of G, find a 2-chain subgraph cover of G such that one of two chain subgraphs has no edges in F.

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Acknowledgments

We are grateful to anonymous referees for careful reading and helpful comments. A part of this work was done while the author was in Tokyo Institute of Technology and supported by JSPS Grant-in-Aid for JSPS Fellows (26\(\cdot \)8924).

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Authors and Affiliations

  1. Department of Information Systems Creation, Kanagawa University, Rokkakubashi 3-27-1, Kanagawa-ku, Kanagawa, 221-8686, Japan

    Asahi Takaoka

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  1. Asahi Takaoka
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Correspondence to Asahi Takaoka .

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Editors and Affiliations

  1. Universiti Teknologi Brunei, Bandar Seri Begawan, Brunei Darussalam

    Sheung-Hung Poon

  2. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Saidur Rahman

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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Takaoka, A. (2017). Recognizing Simple-Triangle Graphs by Restricted 2-Chain Subgraph Cover. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_14

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  • DOI: https://doi.org/10.1007/978-3-319-53925-6_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53924-9

  • Online ISBN: 978-3-319-53925-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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