Almost all string graphs are intersection graphs of plane convex sets

@inproceedings{Pach2018AlmostAS,
  title={Almost all string graphs are intersection graphs of plane convex sets},
  author={J. Pach and B. Reed and Y. Yuditsky},
  booktitle={SoCG},
  year={2018}
}
A {\em string graph} is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of {\em almost all} string graphs on $n$ vertices can be partitioned into {\em five} cliques such that some pair of them is not connected by any edge ($n\rightarrow\infty$). We also show… Expand

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References

SHOWING 1-10 OF 37 REFERENCES
Recognizing string graphs in NP
On intersection representations of co-planar graphs
Decidability of string graphs
How Many Ways Can One Draw a Graph?
How Many Ways Can One Draw A Graph?
The fine structure of octahedron-free graphs
Hereditary and Monotone Properties of Graphs
Almost all Berge Graphs are Perfect
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