Lower bounds to Helly numbers of line transversals to disjoint congruent balls

Cited 3 time in webofscience Cited 0 time in scopus
  • Hit : 546
  • Download : 0
DC FieldValueLanguage
dc.contributor.authorCheong, Otfriedko
dc.contributor.authorGoaoc, Xavierko
dc.contributor.authorHolmsen, Andreasko
dc.date.accessioned2013-03-12T04:51:51Z-
dc.date.available2013-03-12T04:51:51Z-
dc.date.created2012-09-27-
dc.date.created2012-09-27-
dc.date.issued2012-08-
dc.identifier.citationISRAEL JOURNAL OF MATHEMATICS, v.190, no.1, pp.213 - 228-
dc.identifier.issn0021-2172-
dc.identifier.urihttp://hdl.handle.net/10203/101366-
dc.description.abstractA line l is a transversal to a family F of convex objects in a"e (d) if it intersects every member of F. In this paper we show that for every integer d >= 3 there exists a family of 2d-1 pairwise disjoint unit balls in a"e (d) with the property that every subfamily of size 2d - 2 admits a transversal, yet any line misses at least one member of the family. This answers a question of Danzer from 1957. Crucial to the proof is the notion of a pinned transversal, which means an isolated point in the space of transversals. Here we investigate minimal pinning configurations and construct a family F of 2d-1 disjoint unit balls in R-d with the following properties: (i) The space of transversals to F is a single point and (ii) the space of transversals to any proper subfamily of F is a connected set with non-empty interior.-
dc.languageEnglish-
dc.publisherHEBREW UNIV MAGNES PRESS-
dc.subjectCOMMON TRANSVERSALS-
dc.subjectUNIT BALLS-
dc.subjectTHEOREM-
dc.subjectCONJECTURE-
dc.subjectGRUNBAUM-
dc.titleLower bounds to Helly numbers of line transversals to disjoint congruent balls-
dc.typeArticle-
dc.identifier.wosid000307305300010-
dc.identifier.scopusid2-s2.0-84863946262-
dc.type.rimsART-
dc.citation.volume190-
dc.citation.issue1-
dc.citation.beginningpage213-
dc.citation.endingpage228-
dc.citation.publicationnameISRAEL JOURNAL OF MATHEMATICS-
dc.identifier.doi10.1007/s11856-011-0179-1-
dc.contributor.localauthorCheong, Otfried-
dc.contributor.localauthorHolmsen, Andreas-
dc.contributor.nonIdAuthorGoaoc, Xavier-
dc.type.journalArticleArticle-
dc.subject.keywordPlusCOMMON TRANSVERSALS-
dc.subject.keywordPlusUNIT BALLS-
dc.subject.keywordPlusTHEOREM-
dc.subject.keywordPlusCONJECTURE-
dc.subject.keywordPlusGRUNBAUM-
Appears in Collection
CS-Journal Papers(저널논문)MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 3 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0