{"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 3/2(n-1), and that this bound is best possible for infinitely many values of n."}],"language":[{"iso":"eng"}],"day":"21","year":"2018","date_published":"2018-01-21T00:00:00Z","_id":"433","type":"conference","oa_version":"Submitted Version","publication_status":"published","scopus_import":"1","doi":"10.1007/978-3-319-73915-1_14","title":"Thrackles: An improved upper bound","date_created":"2018-12-11T11:46:27Z","status":"public","related_material":{"record":[{"status":"public","relation":"later_version","id":"5857"}]},"corr_author":"1","citation":{"ista":"Fulek R, Pach J. 2018. Thrackles: An improved upper bound. GD: Graph Drawing and Network Visualization, LNCS, vol. 10692, 160–166.","chicago":"Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound,” 10692:160–66. Springer, 2018. <a href=\"https://doi.org/10.1007/978-3-319-73915-1_14\">https://doi.org/10.1007/978-3-319-73915-1_14</a>.","ama":"Fulek R, Pach J. Thrackles: An improved upper bound. In: Vol 10692. Springer; 2018:160-166. doi:<a href=\"https://doi.org/10.1007/978-3-319-73915-1_14\">10.1007/978-3-319-73915-1_14</a>","short":"R. Fulek, J. Pach, in:, Springer, 2018, pp. 160–166.","apa":"Fulek, R., &#38; Pach, J. (2018). Thrackles: An improved upper bound (Vol. 10692, pp. 160–166). Presented at the GD: Graph Drawing and Network Visualization, Boston, MA, United States: Springer. <a href=\"https://doi.org/10.1007/978-3-319-73915-1_14\">https://doi.org/10.1007/978-3-319-73915-1_14</a>","mla":"Fulek, Radoslav, and János Pach. <i>Thrackles: An Improved Upper Bound</i>. Vol. 10692, Springer, 2018, pp. 160–66, doi:<a href=\"https://doi.org/10.1007/978-3-319-73915-1_14\">10.1007/978-3-319-73915-1_14</a>.","ieee":"R. Fulek and J. Pach, “Thrackles: An improved upper bound,” presented at the GD: Graph Drawing and Network Visualization, Boston, MA, United States, 2018, vol. 10692, pp. 160–166."},"alternative_title":["LNCS"],"intvolume":"     10692","publisher":"Springer","date_updated":"2025-07-10T11:52:38Z","department":[{"_id":"UlWa"}],"publist_id":"7390","article_processing_charge":"No","arxiv":1,"conference":{"location":"Boston, MA, United States","name":"GD: Graph Drawing and Network Visualization","end_date":"2017-09-27","start_date":"201-09-25"},"external_id":{"arxiv":["1708.08037"]},"page":"160 - 166","main_file_link":[{"url":"https://arxiv.org/abs/1708.08037","open_access":"1"}],"month":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","volume":10692,"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","full_name":"Pach, János","last_name":"Pach"}],"oa":1}