{"year":"2017","publisher":"Elsevier","language":[{"iso":"eng"}],"department":[{"_id":"UlWa"}],"month":"01","date_published":"2017-01-01T00:00:00Z","article_processing_charge":"No","citation":{"apa":"Fulek, R., Mojarrad, H., Naszódi, M., Solymosi, J., Stich, S., &#38; Szedlák, M. (2017). On the existence of ordinary triangles. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2017.07.002\">https://doi.org/10.1016/j.comgeo.2017.07.002</a>","short":"R. Fulek, H. Mojarrad, M. Naszódi, J. Solymosi, S. Stich, M. Szedlák, Computational Geometry: Theory and Applications 66 (2017) 28–31.","ista":"Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. 2017. On the existence of ordinary triangles. Computational Geometry: Theory and Applications. 66, 28–31.","ieee":"R. Fulek, H. Mojarrad, M. Naszódi, J. Solymosi, S. Stich, and M. Szedlák, “On the existence of ordinary triangles,” <i>Computational Geometry: Theory and Applications</i>, vol. 66. Elsevier, pp. 28–31, 2017.","mla":"Fulek, Radoslav, et al. “On the Existence of Ordinary Triangles.” <i>Computational Geometry: Theory and Applications</i>, vol. 66, Elsevier, 2017, pp. 28–31, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.07.002\">10.1016/j.comgeo.2017.07.002</a>.","ama":"Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. On the existence of ordinary triangles. <i>Computational Geometry: Theory and Applications</i>. 2017;66:28-31. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.07.002\">10.1016/j.comgeo.2017.07.002</a>","chicago":"Fulek, Radoslav, Hossein Mojarrad, Márton Naszódi, József Solymosi, Sebastian Stich, and May Szedlák. “On the Existence of Ordinary Triangles.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.comgeo.2017.07.002\">https://doi.org/10.1016/j.comgeo.2017.07.002</a>."},"page":"28 - 31","date_created":"2018-12-11T11:48:32Z","publist_id":"6861","oa":1,"isi":1,"status":"public","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Let P be a finite point set in the plane. A cordinary triangle in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P . Motivated by a question of Erdös, and answering a question of de Zeeuw, we prove that there exists a constant c &gt; 0such that P contains a c-ordinary triangle, provided that P is not contained in the union of two lines. Furthermore, the number of c-ordinary triangles in P is Ω(| P |). "}],"type":"journal_article","external_id":{"isi":["000412039700003"]},"_id":"793","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"publication_identifier":{"issn":["09257721"]},"author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","last_name":"Fulek","full_name":"Fulek, Radoslav","first_name":"Radoslav","orcid":"0000-0001-8485-1774"},{"full_name":"Mojarrad, Hossein","last_name":"Mojarrad","first_name":"Hossein"},{"first_name":"Márton","last_name":"Naszódi","full_name":"Naszódi, Márton"},{"first_name":"József","full_name":"Solymosi, József","last_name":"Solymosi"},{"first_name":"Sebastian","full_name":"Stich, Sebastian","last_name":"Stich"},{"first_name":"May","full_name":"Szedlák, May","last_name":"Szedlák"}],"ec_funded":1,"publication_status":"published","title":"On the existence of ordinary triangles","doi":"10.1016/j.comgeo.2017.07.002","quality_controlled":"1","day":"01","publication":"Computational Geometry: Theory and Applications","date_updated":"2023-09-27T12:15:16Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1701.08183"}],"volume":66,"intvolume":"        66","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"}