{"publist_id":"7390","publisher":"Springer","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"}],"related_material":{"record":[{"status":"public","id":"5857","relation":"later_version"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":1,"doi":"10.1007/978-3-319-73915-1_14","citation":{"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>","ieee":"R. Fulek and J. Pach, “Thrackles: An improved upper bound,” presented at the GD 2017: Graph Drawing and Network Visualization, Boston, MA, United States, 2018, vol. 10692, pp. 160–166.","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 2017: 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>","ista":"Fulek R, Pach J. 2018. Thrackles: An improved upper bound. GD 2017: Graph Drawing and Network Visualization, LNCS, vol. 10692, 160–166.","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>."},"conference":{"end_date":"2017-09-27","name":"GD 2017: Graph Drawing and Network Visualization","start_date":"201-09-25","location":"Boston, MA, United States"},"status":"public","day":"21","date_published":"2018-01-21T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.08037"}],"quality_controlled":"1","external_id":{"arxiv":["1708.08037"]},"alternative_title":["LNCS"],"intvolume":"     10692","oa":1,"oa_version":"Submitted Version","publication_status":"published","type":"conference","year":"2018","author":[{"orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav","last_name":"Fulek","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","first_name":"Radoslav"},{"full_name":"Pach, János","last_name":"Pach","first_name":"János"}],"title":"Thrackles: An improved upper bound","_id":"433","department":[{"_id":"UlWa"}],"date_created":"2018-12-11T11:46:27Z","volume":10692,"page":"160 - 166","date_updated":"2023-08-24T14:39:32Z","month":"01"}