[{"oa":1,"quality_controlled":"1","date_created":"2018-12-11T11:46:27Z","date_published":"2018-01-21T00:00:00Z","page":"160 - 166","uri_base":"https://research-explorer.ista.ac.at","dc":{"publisher":["Springer"],"type":["info:eu-repo/semantics/conferenceObject","doc-type:conferenceObject","text","http://purl.org/coar/resource_type/c_5794"],"date":["2018"],"identifier":["https://research-explorer.ista.ac.at/record/433"],"description":["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."],"source":["Fulek R, Pach J. Thrackles: An improved upper bound. In: Vol 10692. Springer; 2018:160-166. doi:10.1007/978-3-319-73915-1_14"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-73915-1_14","info:eu-repo/semantics/altIdentifier/arxiv/1708.08037"],"title":["Thrackles: An improved upper bound","LNCS"],"language":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"creator":["Fulek, Radoslav","Pach, János"]},"day":"21","external_id":{"arxiv":[]},"author":[{"id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","first_name":"Radoslav","last_name":"Fulek","orcid":"0000-0001-8485-1774"},{"first_name":"János","last_name":"Pach"}],"publist_id":"7390","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","dini_type":"doc-type:conferenceObject","citation":{"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., & 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. https://doi.org/10.1007/978-3-319-73915-1_14","mla":"Fulek, Radoslav, and János Pach. Thrackles: An Improved Upper Bound. Vol. 10692, Springer, 2018, pp. 160–66, doi:10.1007/978-3-319-73915-1_14.","ista":"Fulek R, Pach J. 2018. Thrackles: An improved upper bound. GD 2017: 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. https://doi.org/10.1007/978-3-319-73915-1_14."},"intvolume":" 10692","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.08037"}],"scopus_import":1,"alternative_title":[],"oa_version":"Submitted Version","abstract":[{"lang":"eng"}],"volume":10692,"related_material":{"record":[{"relation":"later_version","id":"5857","status":"public"}]},"language":[{}],"publication_status":"published","status":"public","conference":{"start_date":"201-09-25","location":"Boston, MA, United States","end_date":"2017-09-27","name":"GD 2017: Graph Drawing and Network Visualization"},"type":"conference","_id":"433","department":[{"_id":"UlWa","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"creator":{"login":"apreinsp","id":"4435EBFC-F248-11E8-B48F-1D18A9856A87"},"date_updated":"2023-08-24T14:39:32Z"}]