# 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}
}
• Published in SoCG 2018
• Computer Science, Mathematics
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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