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Characterization and a 2D Visualization of B\(_{0}\)-VPG Cocomparability Graphs

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Graph Drawing and Network Visualization (GD 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12590))

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Abstract

\(B_{0}\)-VPG graphs are intersection graphs of vertical and horizontal line segments on a plane. Cohen, Golumbic, Trotter, and Wang [Order, 2016] pose the question of characterizing B\(_{0}\)-VPG permutation graphs. We respond here by characterizing B\(_{0}\)-VPG cocomparability graphs. This characterization also leads to a polynomial time recognition and B\(_{0}\)-VPG drawing algorithm for the class. Our B\(_{0}\)-VPG drawing algorithm starts by fixing any one of the many posets P whose cocomparability graph is the input graph G. The drawing we obtain not only visualizes G in that one can distinguish comparable pairs from incomparable ones, but one can also identify which among a comparable pair is larger in P from this visualization.

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Notes

  1. 1.

    Details of the proof can be found in the Appendix section of the full version [26].

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Authors and Affiliations

  1. Indian Institute of Technology Palakkad, Palakkad, India

    Sreejith K. Pallathumadam & Deepak Rajendraprasad

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  1. Sreejith K. Pallathumadam
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  2. Deepak Rajendraprasad
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Correspondence to Sreejith K. Pallathumadam .

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Editors and Affiliations

  1. LaBRI, University of Bordeaux, Talence, France

    David Auber

  2. Charles University, Prague, Czech Republic

    Pavel Valtr

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Pallathumadam, S.K., Rajendraprasad, D. (2020). Characterization and a 2D Visualization of B\(_{0}\)-VPG Cocomparability Graphs. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_16

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  • DOI: https://doi.org/10.1007/978-3-030-68766-3_16

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  • Online ISBN: 978-3-030-68766-3

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