[{"project":[{"name":"The Wittgenstein Prize","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"article_processing_charge":"No","oa_version":"Preprint","date_published":"2020-06-05T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1803.06710"}],"page":"888-917","month":"06","publisher":"Springer Nature","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"doi":"10.1007/s00454-020-00213-z","volume":63,"year":"2020","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"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→∞). 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."}],"day":"05","article_type":"original","oa":1,"publication":"Discrete and Computational Geometry","date_created":"2020-06-14T22:00:51Z","intvolume":" 63","type":"journal_article","status":"public","quality_controlled":"1","language":[{"iso":"eng"}],"scopus_import":1,"citation":{"ista":"Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917.","apa":"Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. *Discrete and Computational Geometry*. Springer Nature. https://doi.org/10.1007/s00454-020-00213-z","mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” *Discrete and Computational Geometry*, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z.","chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” *Discrete and Computational Geometry*. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z.","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","ama":"Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. *Discrete and Computational Geometry*. 2020;63(4):888-917. doi:10.1007/s00454-020-00213-z","ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” *Discrete and Computational Geometry*, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020."},"date_updated":"2021-01-12T08:16:15Z","external_id":{"arxiv":["1803.06710"]},"author":[{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","first_name":"János","last_name":"Pach"},{"first_name":"Bruce","last_name":"Reed","full_name":"Reed, Bruce"},{"full_name":"Yuditsky, Yelena","first_name":"Yelena","last_name":"Yuditsky"}],"issue":"4","_id":"7962","title":"Almost all string graphs are intersection graphs of plane convex sets","publication_status":"published","department":[{"_id":"HeEd"}]}]