{"author":[{"orcid":"0000-0001-8485-1774","last_name":"Fulek","full_name":"Fulek, Radoslav","first_name":"Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mojarrad","full_name":"Mojarrad, Hossein","first_name":"Hossein"},{"first_name":"Márton","full_name":"Naszódi, Márton","last_name":"Naszódi"},{"first_name":"József","full_name":"Solymosi, József","last_name":"Solymosi"},{"full_name":"Stich, Sebastian","last_name":"Stich","first_name":"Sebastian"},{"first_name":"May","full_name":"Szedlák, May","last_name":"Szedlák"}],"type":"journal_article","year":"2017","volume":66,"page":"28 - 31","date_updated":"2023-09-27T12:15:16Z","month":"01","date_created":"2018-12-11T11:48:32Z","department":[{"_id":"UlWa"}],"_id":"793","title":"On the existence of ordinary triangles","intvolume":"        66","publication_status":"published","oa":1,"oa_version":"Submitted Version","isi":1,"project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1701.08183"}],"date_published":"2017-01-01T00:00:00Z","publication_identifier":{"issn":["09257721"]},"ec_funded":1,"status":"public","day":"01","publication":"Computational Geometry: Theory and Applications","external_id":{"isi":["000412039700003"]},"quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","language":[{"iso":"eng"}],"article_processing_charge":"No","publisher":"Elsevier","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 |). "}],"publist_id":"6861","citation":{"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.","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>.","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>.","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.","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."},"doi":"10.1016/j.comgeo.2017.07.002"}