---
_id: '1064'
abstract:
- lang: eng
  text: 'In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by
    P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it
    is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot
    be separated into two subfamilies by a straight line disjoint from the disks.
    In this note we show that essentially the same idea may work for different analogues
    and generalizations of their result. In particular, we prove the following: Given
    a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety
    coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate
    of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane
    disjoint from the homothets.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Arseniy
  full_name: Akopyan, Arseniy
  id: 430D2C90-F248-11E8-B48F-1D18A9856A87
  last_name: Akopyan
  orcid: 0000-0002-2548-617X
- first_name: Alexey
  full_name: Balitskiy, Alexey
  last_name: Balitskiy
- first_name: Mikhail
  full_name: Grigorev, Mikhail
  last_name: Grigorev
citation:
  ama: Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W.
    Goodman and R.E. Goodman. <i>Discrete &#38; Computational Geometry</i>. 2018;59(4):1001-1009.
    doi:<a href="https://doi.org/10.1007/s00454-017-9883-x">10.1007/s00454-017-9883-x</a>
  apa: Akopyan, A., Balitskiy, A., &#38; Grigorev, M. (2018). On the circle covering
    theorem by A.W. Goodman and R.E. Goodman. <i>Discrete &#38; Computational Geometry</i>.
    Springer. <a href="https://doi.org/10.1007/s00454-017-9883-x">https://doi.org/10.1007/s00454-017-9883-x</a>
  chicago: Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle
    Covering Theorem by A.W. Goodman and R.E. Goodman.” <i>Discrete &#38; Computational
    Geometry</i>. Springer, 2018. <a href="https://doi.org/10.1007/s00454-017-9883-x">https://doi.org/10.1007/s00454-017-9883-x</a>.
  ieee: A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem
    by A.W. Goodman and R.E. Goodman,” <i>Discrete &#38; Computational Geometry</i>,
    vol. 59, no. 4. Springer, pp. 1001–1009, 2018.
  ista: Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by
    A.W. Goodman and R.E. Goodman. Discrete &#38; Computational Geometry. 59(4), 1001–1009.
  mla: Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and
    R.E. Goodman.” <i>Discrete &#38; Computational Geometry</i>, vol. 59, no. 4, Springer,
    2018, pp. 1001–09, doi:<a href="https://doi.org/10.1007/s00454-017-9883-x">10.1007/s00454-017-9883-x</a>.
  short: A. Akopyan, A. Balitskiy, M. Grigorev, Discrete &#38; Computational Geometry
    59 (2018) 1001–1009.
corr_author: '1'
date_created: 2018-12-11T11:49:57Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2026-05-20T10:19:33Z
day: '01'
ddc:
- '516'
- '000'
department:
- _id: HeEd
doi: 10.1007/s00454-017-9883-x
ec_funded: 1
external_id:
  isi:
  - '000432205500011'
file:
- access_level: open_access
  content_type: application/pdf
  creator: dernst
  date_created: 2019-01-18T09:27:36Z
  date_updated: 2019-01-18T09:27:36Z
  file_id: '5844'
  file_name: 2018_DiscreteComp_Akopyan.pdf
  file_size: 482518
  relation: main_file
  success: 1
file_date_updated: 2019-01-18T09:27:36Z
has_accepted_license: '1'
intvolume: '        59'
isi: 1
issue: '4'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1001-1009
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Discrete & Computational Geometry
publication_identifier:
  eissn:
  - 1432-0444
  issn:
  - 0179-5376
publication_status: published
publisher: Springer
publist_id: '6324'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the circle covering theorem by A.W. Goodman and R.E. Goodman
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2018'
...