---
_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'
...