---
res:
bibo_abstract:
- '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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Arseniy
foaf_name: Akopyan, Arseniy
foaf_surname: Akopyan
foaf_workInfoHomepage: http://www.librecat.org/personId=430D2C90-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Alexey
foaf_name: Balitskiy, Alexey
foaf_surname: Balitskiy
- foaf_Person:
foaf_givenName: Mikhail
foaf_name: Grigorev, Mikhail
foaf_surname: Grigorev
bibo_doi: 10.1007/s00454-017-9883-x
bibo_issue: '4'
bibo_volume: 59
dct_date: 2018^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/01795376
dct_language: eng
dct_publisher: Springer@
dct_title: On the circle covering theorem by A.W. Goodman and R.E. Goodman@
...