Transversals in Superdisjoint T(3)-families of Translates

Autor:	Aladár Heppes
Rok vydání:	2010
Předmět:	Combinatorics Discrete mathematics Transversal (geometry) Computational Theory and Mathematics Common line Discrete Mathematics and Combinatorics Geometry and Topology Disjoint sets Convex domain Concentric Theoretical Computer Science Mathematics
Zdroj:	Discrete & Computational Geometry. 45:321-328
ISSN:	1432-0444 0179-5376
DOI:	10.1007/s00454-010-9292-x
Popis:	Let K denote an oval, a centrally symmetric compact convex domain with non-empty interior. A family of translates of K is said to have property T(k) if for every subset of at most k translates there exists a common line transversal intersecting all of them. Property T means that a transversal exists for all members of the family. Two translates, K i and K j are said to be φ-disjoint, φ>0, if the concentric φ-enlarged copies of K i and K j are disjoint. It is well known that in a φ-disjoint family of congruent discs T(3)⇒T if $\varphi>\sqrt{2}$, and $T(3)\not\Rightarrow T$ if $\varphi
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::395f8ea177bd9b65e24f89dbf47f703e https://doi.org/10.1007/s00454-010-9292-x Zobrazit plný text záznamu Full text from SpringerLink