@inproceedings{6411d0925c854871984db5be95116fc8,

title = "Almost all string graphs are intersection graphs of plane convex sets",

abstract = "A 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 almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n α→ ∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.",

keywords = "Intersection graph, Plane convex set, String graph",

author = "J{\'a}nos Pach and Bruce Reed and Yelena Yuditsky",

note = "Funding Information: Supported by Swiss National Science Foundation Grants 200021-165977 and 200020-162884. Publisher Copyright: {\textcopyright} J{\'a}nos Pach, Bruce Reed, and Yelena Yuditsky; licensed under Creative Commons License CC-BY 34th Symposium on Computational Geometry (SoCG 2018).; 34th International Symposium on Computational Geometry, SoCG 2018 ; Conference date: 11-06-2018 Through 14-06-2018",

year = "2018",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.SoCG.2018.68",

language = "English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

pages = "681--6814",

editor = "Toth, {Csaba D.} and Bettina Speckmann",

booktitle = "34th International Symposium on Computational Geometry, SoCG 2018",

address = "Germany",

}