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Drawing Bipartite Graphs in Two Layers with Specified Crossings

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Algorithms and Discrete Applied Mathematics (CALDAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11394))

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Abstract

We give a polynomial-time algorithm to decide whether a bipartite graph admits a two-layer drawing in the plane such that a specified subset of pairs of edges cross. This is a generalization of the problem of recognizing permutation graphs, and we generalize the characterization of permutation graphs.

S. K. Ghosh—The author’s work is funded by SERB, Government of India through a grant under MATRICS.

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References

  1. Diwan, A.A., Roy, B., Ghosh, S.K.: Two-layer drawings of bipartite graphs. Electron. Notes Discret. Math. 61, 351–357 (2017). https://doi.org/10.1016/j.endm.2017.06.059

    Article  MATH  Google Scholar 

  2. Eades, P., Whitesides, S.: Drawing graphs in two layers. Theor. Comput. Sci. 131(2), 361–374 (1994). https://doi.org/10.1016/0304-3975(94)90179-1

    Article  MathSciNet  MATH  Google Scholar 

  3. Finocchi, I.: Crossing-constrained hierarchical drawings. J. Discret. Algorithms 4, 299–312 (2006). https://doi.org/10.1016/j.jda.2005.06.001

    Article  MathSciNet  MATH  Google Scholar 

  4. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Annals of Discrete Mathematics, vol. 57, 2nd edn. Elsevier, New York (2004). https://doi.org/10.1016/S0167-5060(04)80051-7

    Book  MATH  Google Scholar 

  5. Gilmore, P.C., Hoffman, A.J.: A characterization of comparability graphs and of interval graphs. Can. J. Math. 16, 539–548 (1964)

    Article  MathSciNet  Google Scholar 

  6. Kratochvíl, J.: String graphs II. Recognizing string graphs is NP-Hard. J. Combin. Theory Ser. B 52, 67–78 (1991). https://doi.org/10.1016/0095-8956(91)90091-W

    Article  MathSciNet  MATH  Google Scholar 

  7. Kynčl, J.: Simple realizability of complete abstract topological graphs in P. Discret. Comput. Geom. 45, 383–399 (2011). https://doi.org/10.1007/s00454-010-9320-x

    Article  MathSciNet  MATH  Google Scholar 

  8. Pnueli, A., Lempel, A., Even, S.: Transitive orientation of graphs and identification of permutation graphs. Can. J. Math. 23, 160–175 (1971). https://doi.org/10.4153/CJM-1971-016-5

    Article  MathSciNet  MATH  Google Scholar 

  9. Spinrad, J.: On comparability and permutation graphs. SIAM J. Comput. 14(3), 658–670 (1985). https://doi.org/10.1137/0214048

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Ajit A. Diwan

  2. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    Bodhayan Roy

  3. Department of Computer Science, Ramakrishna Mission Vivekananda Educational and Research Institute, Belur, Howrah, 711202, India

    Subir Kumar Ghosh

Authors
  1. Ajit A. Diwan
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  2. Bodhayan Roy
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  3. Subir Kumar Ghosh
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Corresponding author

Correspondence to Ajit A. Diwan .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology, Kharagpur, India

    Sudebkumar Prasant Pal

  2. Cochin University of Science and Technology, Cochin, India

    Ambat Vijayakumar

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Diwan, A.A., Roy, B., Ghosh, S.K. (2019). Drawing Bipartite Graphs in Two Layers with Specified Crossings. In: Pal, S., Vijayakumar, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2019. Lecture Notes in Computer Science(), vol 11394. Springer, Cham. https://doi.org/10.1007/978-3-030-11509-8_9

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  • DOI: https://doi.org/10.1007/978-3-030-11509-8_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11508-1

  • Online ISBN: 978-3-030-11509-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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