---
_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
article_processing_charge: No
arxiv: 1
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:<a href="https://doi.org/10.1007/978-3-319-73915-1_14">10.1007/978-3-319-73915-1_14</a>'
  apa: 'Fulek, R., &#38; Pach, J. (2018). Thrackles: An improved upper bound (Vol.
    10692, pp. 160–166). Presented at the GD: 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>'
  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>.'
  ieee: 'R. Fulek and J. Pach, “Thrackles: An improved upper bound,” presented at
    the GD: 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: 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>.'
  short: R. Fulek, J. Pach, in:, Springer, 2018, pp. 160–166.
conference:
  end_date: 2017-09-27
  location: Boston, MA, United States
  name: 'GD: Graph Drawing and Network Visualization'
  start_date: 201-09-25
corr_author: '1'
date_created: 2018-12-11T11:46:27Z
date_published: 2018-01-21T00:00:00Z
date_updated: 2026-04-16T09:48:11Z
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'
...