--- _id: '433' 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.' alternative_title: - LNCS author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: János full_name: Pach, János last_name: Pach citation: ama: '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' 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' 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.' 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.' 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. Thrackles: An Improved Upper Bound. Vol. 10692, Springer, 2018, pp. 160–66, doi:10.1007/978-3-319-73915-1_14.' short: R. Fulek, J. Pach, in:, Springer, 2018, pp. 160–166. conference: end_date: 2017-09-27 location: Boston, MA, United States name: 'GD 2017: Graph Drawing and Network Visualization' start_date: 201-09-25 date_created: 2018-12-11T11:46:27Z date_published: 2018-01-21T00:00:00Z date_updated: 2023-08-24T14:39:32Z day: '21' department: - _id: UlWa doi: 10.1007/978-3-319-73915-1_14 external_id: arxiv: - '1708.08037' intvolume: ' 10692' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.08037 month: '01' oa: 1 oa_version: Submitted Version page: 160 - 166 publication_status: published publisher: Springer publist_id: '7390' quality_controlled: '1' related_material: record: - id: '5857' relation: later_version status: public scopus_import: 1 status: public title: 'Thrackles: An improved upper bound' type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 10692 year: '2018' ...