{"doi":"10.1016/j.dam.2018.12.025","publication":"Discrete Applied Mathematics","publication_identifier":{"issn":["0166218X"]},"article_type":"original","intvolume":"       259","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.08037"}],"language":[{"iso":"eng"}],"year":"2019","day":"30","date_updated":"2023-08-24T14:39:33Z","external_id":{"isi":["000466061100020"],"arxiv":["1708.08037"]},"oa":1,"publisher":"Elsevier","abstract":[{"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.","lang":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"oa_version":"Preprint","page":"266-231","article_processing_charge":"No","type":"journal_article","issue":"4","department":[{"_id":"UlWa"}],"publication_status":"published","quality_controlled":"1","volume":259,"_id":"5857","status":"public","citation":{"short":"R. Fulek, J. Pach, Discrete Applied Mathematics 259 (2019) 266–231.","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>","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>.","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>.","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>","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.","ista":"Fulek R, Pach J. 2019. Thrackles: An improved upper bound. Discrete Applied Mathematics. 259(4), 266–231."},"month":"04","author":[{"first_name":"Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav"},{"first_name":"János","last_name":"Pach","full_name":"Pach, János"}],"related_material":{"record":[{"status":"public","id":"433","relation":"earlier_version"}]},"scopus_import":"1","date_created":"2019-01-20T22:59:17Z","date_published":"2019-04-30T00:00:00Z","title":"Thrackles: An improved upper bound","project":[{"grant_number":"M02281","call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs","_id":"261FA626-B435-11E9-9278-68D0E5697425"}]}