MANY POLYTOPES MEETING THE CONJECTURED HIRSCH BOUND

Authors
HOLT FB KLEE V
Citation
Fb. Holt et V. Klee, MANY POLYTOPES MEETING THE CONJECTURED HIRSCH BOUND, Discrete & computational geometry, 20(1), 1998, pp. 1-17
Citations number
9
Categorie Soggetti
Computer Science Theory & Methods",Mathematics,"Computer Science Theory & Methods",Mathematics
Journal title
Discrete & computational geometry → ACNP
ISSN journal
01795376
Volume
20
Issue
1
Year of publication
1998
Pages
1 - 17
Database
ISI
SICI code
0179-5376(1998)20:1<1:MPMTCH>2.0.ZU;2-F
Abstract
The still open Hirsch conjecture asserts that Delta(d, n) less than or equal to n - d for all n > d greater than or equal to 2, where Delta( d, n) denotes the maximum edge-diameter of (convex) d-polytopes with n facets. This paper adds to the list of pairs (d, n) that are known to be H-sharp in the sense that Delta(d, n) greater than or equal to n - d. In particular, it is proved that Delta(d, n) greater than or equal to n - d for all n > d greater than or equal to 14.