Cutting a set of disks by a line with leaving many intact disks in both sides

Authors
Maehara, H Oshiro, A
Citation
H. Maehara et A. Oshiro, Cutting a set of disks by a line with leaving many intact disks in both sides, J COMB TH A, 90(1), 2000, pp. 235-240
Citations number
2
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES A
ISSN journal
00973165 → ACNP
Volume
90
Issue
1
Year of publication
2000
Pages
235 - 240
Database
ISI
SICI code
0097-3165(200004)90:1<235:CASODB>2.0.ZU;2-F
Abstract
Cut by a line the union of given disjoint disks in the plane so that both s ides of the line contain many intact disks. At least how many intact disks can we leave in either side? It is proved that there is a family of infinit ely many disjoint disks in the plans for which every line has a side that c ontains at most one intact disk. On the other hand, for any family of n dis joint disks. there is a circle C such that both the interior and the exteri or of C contain n/4 - o(n) intact disks.(C) 2000 Academic Press.