{"date_created":"2019-01-20T22:59:17Z","abstract":[{"lang":"eng","text":"A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is [Formula presented](n−1), and that this bound is best possible for infinitely many values of n."}],"volume":259,"_id":"5857","scopus_import":"1","oa":1,"publication_status":"published","publication":"Discrete Applied Mathematics","language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"article_processing_charge":"No","publisher":"Elsevier","day":"30","department":[{"_id":"UlWa"}],"status":"public","external_id":{"arxiv":["1708.08037"],"isi":["000466061100020"]},"author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","full_name":"Fulek, Radoslav","last_name":"Fulek","first_name":"Radoslav","orcid":"0000-0001-8485-1774"},{"first_name":"János","last_name":"Pach","full_name":"Pach, János"}],"oa_version":"Preprint","date_updated":"2023-08-24T14:39:33Z","page":"266-231","doi":"10.1016/j.dam.2018.12.025","article_type":"original","type":"journal_article","issue":"4","title":"Thrackles: An improved upper bound","quality_controlled":"1","related_material":{"record":[{"id":"433","status":"public","relation":"earlier_version"}]},"project":[{"name":"Eliminating intersections in drawings of graphs","call_identifier":"FWF","grant_number":"M02281","_id":"261FA626-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.08037"}],"intvolume":"       259","citation":{"apa":"Fulek, R., &#38; Pach, J. (2019). Thrackles: An improved upper bound. <i>Discrete Applied Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.dam.2018.12.025\">https://doi.org/10.1016/j.dam.2018.12.025</a>","ista":"Fulek R, Pach J. 2019. Thrackles: An improved upper bound. Discrete Applied Mathematics. 259(4), 266–231.","chicago":"Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound.” <i>Discrete Applied Mathematics</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.dam.2018.12.025\">https://doi.org/10.1016/j.dam.2018.12.025</a>.","ieee":"R. Fulek and J. Pach, “Thrackles: An improved upper bound,” <i>Discrete Applied Mathematics</i>, vol. 259, no. 4. Elsevier, pp. 266–231, 2019.","ama":"Fulek R, Pach J. Thrackles: An improved upper bound. <i>Discrete Applied Mathematics</i>. 2019;259(4):266-231. doi:<a href=\"https://doi.org/10.1016/j.dam.2018.12.025\">10.1016/j.dam.2018.12.025</a>","mla":"Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound.” <i>Discrete Applied Mathematics</i>, vol. 259, no. 4, Elsevier, 2019, pp. 266–231, doi:<a href=\"https://doi.org/10.1016/j.dam.2018.12.025\">10.1016/j.dam.2018.12.025</a>.","short":"R. Fulek, J. Pach, Discrete Applied Mathematics 259 (2019) 266–231."},"date_published":"2019-04-30T00:00:00Z","month":"04","year":"2019","publication_identifier":{"issn":["0166218X"]}}