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