On a topological fractional Helly theorem
| dc.creator | Hell, Stephan | |
| dc.date | 2005-06-20 | |
| dc.date.accessioned | 2026-07-07T05:20:52Z | |
| dc.date.available | 2026-07-07T05:20:52Z | |
| dc.description | We prove a new fractional Helly theorem for families of sets obeying topological conditions. More precisely, we show that the nerve of a finite family of open sets (and of subcomplexes of cell complexes) in R^d is k-Leray where k depends on the dimension d and the homological intersection complexity of the family. This implies fractional Helly number k+1 for families F. Moreover, we obtain a topological (p,q)-theorem. Our result contains the (p,q)-theorem for good covers of Alon, Kalai, Matousek, and Meshulam (2003) as a special case. The proof uses a spectral sequence argument. The same method is then used to reprove a homological version of a nerve theorem of Bjoerner. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0506399 | |
| dc.identifier | http://arxiv.org/abs/math/0506399 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75536 | |
| dc.subject | Combinatorics | |
| dc.subject | 52A35 | |
| dc.title | On a topological fractional Helly theorem | |
| dc.type | text |