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Grid Intersection Graphs and Order Dimension

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Abstract

We study subclasses of grid intersection graphs from the perspective of order dimension. We show that partial orders of height two whose comparability graph is a grid intersection graph have order dimension at most four. Starting from this observation we provide a comprehensive study of classes of graphs between grid intersection graphs and bipartite permutation graphs and the containment relation on these classes. Order dimension plays a role in many arguments.

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Acknowledgements

We like to thank the reviewers for useful comments.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Steven Chaplick, Stefan Felsner, Udo Hoffmann & Veit Wiechert

Authors
  1. Steven Chaplick
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  2. Stefan Felsner
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  3. Udo Hoffmann
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  4. Veit Wiechert
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Corresponding author

Correspondence to Udo Hoffmann.

Additional information

Steven Chaplick is supported by ESF EuroGIGA project GraDR, Stefan Felsner is partially supported by DFG grant FE-340/7-2 and ESF EuroGIGA project GraDR, Udo Hoffmann and Veit Wiechert are supported by the Deutsche Forschungsgemeinschaft within the research training group ’Methods for Discrete Structures’ (GRK 1408). The paper is a part of the third author’s dissertation [20].

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Chaplick, S., Felsner, S., Hoffmann, U. et al. Grid Intersection Graphs and Order Dimension. Order 35, 363–391 (2018). https://doi.org/10.1007/s11083-017-9437-0

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