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 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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