--- _id: '5857' 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 [Formula presented](n−1), and that this bound is best possible for infinitely many values of n.' article_processing_charge: No article_type: original 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. Discrete Applied Mathematics. 2019;259(4):266-231. doi:10.1016/j.dam.2018.12.025' apa: 'Fulek, R., & Pach, J. (2019). Thrackles: An improved upper bound. Discrete Applied Mathematics. Elsevier. https://doi.org/10.1016/j.dam.2018.12.025' chicago: 'Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound.” Discrete Applied Mathematics. Elsevier, 2019. https://doi.org/10.1016/j.dam.2018.12.025.' ieee: 'R. Fulek and J. Pach, “Thrackles: An improved upper bound,” Discrete Applied Mathematics, 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.' mla: 'Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound.” Discrete Applied Mathematics, vol. 259, no. 4, Elsevier, 2019, pp. 266–231, doi:10.1016/j.dam.2018.12.025.' short: R. Fulek, J. Pach, Discrete Applied Mathematics 259 (2019) 266–231. date_created: 2019-01-20T22:59:17Z date_published: 2019-04-30T00:00:00Z date_updated: 2023-08-24T14:39:33Z day: '30' department: - _id: UlWa doi: 10.1016/j.dam.2018.12.025 external_id: arxiv: - '1708.08037' isi: - '000466061100020' intvolume: ' 259' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.08037 month: '04' oa: 1 oa_version: Preprint page: 266-231 project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: Discrete Applied Mathematics publication_identifier: issn: - 0166218X publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '433' relation: earlier_version status: public scopus_import: '1' status: public title: 'Thrackles: An improved upper bound' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 259 year: '2019' ...