{"volume":63,"oa_version":"Preprint","page":"888-917","article_processing_charge":"No","title":"Almost all string graphs are intersection graphs of plane convex sets","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"4","month":"06","project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"type":"journal_article","date_published":"2020-06-05T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1803.06710","open_access":"1"}],"isi":1,"date_updated":"2023-08-21T08:49:18Z","language":[{"iso":"eng"}],"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"}],"doi":"10.1007/s00454-020-00213-z","_id":"7962","department":[{"_id":"HeEd"}],"intvolume":"        63","scopus_import":"1","author":[{"last_name":"Pach","first_name":"János","full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"Bruce","full_name":"Reed, Bruce","last_name":"Reed"},{"last_name":"Yuditsky","full_name":"Yuditsky, Yelena","first_name":"Yelena"}],"publisher":"Springer Nature","status":"public","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.","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>.","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>","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>.","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>"},"publication":"Discrete and Computational Geometry","external_id":{"arxiv":["1803.06710"],"isi":["000538229000001"]},"date_created":"2020-06-14T22:00:51Z","year":"2020","publication_status":"published","article_type":"original","oa":1,"quality_controlled":"1","day":"05"}