Grid Intersection Graphs and Order Dimension

@article{Chaplick2018GridIG,
  title={Grid Intersection Graphs and Order Dimension},
  author={Steven Chaplick and Stefan Felsner and Udo Hoffmann and Veit Wiechert},
  journal={Order},
  year={2018},
  volume={35},
  pages={363-391}
}
We study bipartite geometric 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 look at various classes of graphs between grid intersection graph and bipartite permutations graphs and the containment relation on these classes. Order dimension plays a role in many arguments. 

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