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Order

, Volume 35, Issue 2, pp 363–391 | Cite as

Grid Intersection Graphs and Order Dimension

  • Steven Chaplick
  • Stefan Felsner
  • Udo HoffmannEmail author
  • Veit Wiechert
Article
  • 41 Downloads

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.

Keywords

Order dimension Grid intersection graphs 

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Notes

Acknowledgements

We like to thank the reviewers for useful comments.

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Copyright information

© Springer Science+Business Media B.V. 2018

Authors and Affiliations

  • Steven Chaplick
    • 1
  • Stefan Felsner
    • 1
  • Udo Hoffmann
    • 1
    Email author
  • Veit Wiechert
    • 1
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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