{"date_published":"2020-06-05T00:00:00Z","oa_version":"Preprint","intvolume":"        63","oa":1,"title":"Almost all string graphs are intersection graphs of plane convex sets","_id":"7962","date_updated":"2023-08-21T08:49:18Z","volume":63,"citation":{"short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00213-z\">https://doi.org/10.1007/s00454-020-00213-z</a>.","ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” <i>Discrete and Computational Geometry</i>, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020.","mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” <i>Discrete and Computational Geometry</i>, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:<a href=\"https://doi.org/10.1007/s00454-020-00213-z\">10.1007/s00454-020-00213-z</a>.","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.","ama":"Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. <i>Discrete and Computational Geometry</i>. 2020;63(4):888-917. doi:<a href=\"https://doi.org/10.1007/s00454-020-00213-z\">10.1007/s00454-020-00213-z</a>","apa":"Pach, J., Reed, B., &#38; Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00213-z\">https://doi.org/10.1007/s00454-020-00213-z</a>"},"date_created":"2020-06-14T22:00:51Z","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"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."}],"month":"06","article_type":"original","publication":"Discrete and Computational Geometry","external_id":{"arxiv":["1803.06710"],"isi":["000538229000001"]},"publisher":"Springer Nature","day":"05","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"language":[{"iso":"eng"}],"author":[{"first_name":"János","full_name":"Pach, János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"Bruce","full_name":"Reed, Bruce","last_name":"Reed"},{"full_name":"Yuditsky, Yelena","first_name":"Yelena","last_name":"Yuditsky"}],"type":"journal_article","quality_controlled":"1","page":"888-917","scopus_import":"1","year":"2020","article_processing_charge":"No","project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"isi":1,"issue":"4","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1803.06710"}],"status":"public","doi":"10.1007/s00454-020-00213-z"}