No Helly Theorem for Stabbing Translates by Lines in R 3

Autor:	Andreas Holmsen, Jirí Matousek
Rok vydání:	2004
Předmět:	Combinatorics Discrete mathematics Helly's theorem Computational Theory and Mathematics Transversal (combinatorics) Line (geometry) Discrete Mathematics and Combinatorics Convex body Geometry and Topology Disjoint sets Theoretical Computer Science Mathematics
Zdroj:	Discrete and Computational Geometry. 31:405-410
ISSN:	1432-0444 0179-5376
DOI:	10.1007/s00454-003-0796-5
Popis:	For each $n>2$ we construct a convex body $K\subset {\Bbb R}^3$ and a finite family ${\cal F}$ of disjoint translates of $K$ such that any $n-1$ members ${\cal F}$ admit a line transversal, but ${\cal F}$ has no line transversal.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3a7503c9c5919ffb213f24694fd308c4 https://doi.org/10.1007/s00454-003-0796-5 Zobrazit plný text záznamu Full text from SpringerLink