Dropping a vertex or a facet from a convex polytope

Citation
S. Reisner et al., Dropping a vertex or a facet from a convex polytope, FORUM MATH, 13(3), 2001, pp. 359-378
Citations number
13
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
FORUM MATHEMATICUM
ISSN journal
0933-7741 → ACNP
Volume
13
Issue
3
Year of publication
2001
Pages
359 - 378
Database
ISI
SICI code
0933-7741(2001)13:3<359:DAVOAF>2.0.ZU;2-2
Abstract
There exist positive constants c(0) and c(1) = c(1)(n) such that for every 0 < epsilon < 1/2 the following holds: Let P be a convex polytope in R " ha ving N greater than or equal to c(0)"/epsilon vertices x(1) ,..., x(N). The n there exists a subset A subset of {1 ,..., N}, card(A) greater than or eq ual to (1 - 2 epsilon )N, such that for all i is an element of A [GRAPHICS] Also, if P is a convex polytope in R-n having N greater than or equal to c( 0)"/epsilon facets. Let Hit be the half space determined by the facet Fi, w hich contains P (i = 1 ,..., N). Then there exists a subset A subset of {1 ,..., N}, card(A) greater than or equal to (1 - 2 epsilon )N, such that for all i is an element ofA. [GRAPHICS]