---
res:
bibo_abstract:
- 'We show that very weak topological assumptions are enough to ensure the existence
of a Helly-type theorem. More precisely, we show that for any non-negative integers
b and d there exists an integer h(b, d) such that the following holds. If F is
a finite family of subsets of Rd such that βi(∩G)≤b for any G⊊F and every 0 ≤
i ≤ [d/2]-1 then F has Helly number at most h(b, d). Here βi denotes the reduced
Z2-Betti numbers (with singular homology). These topological conditions are sharp:
not controlling any of these [d/2] first Betti numbers allow for families with
unbounded Helly number. Our proofs combine homological non-embeddability results
with a Ramsey-based approach to build, given an arbitrary simplicial complex K,
some well-behaved chain map C*(K)→C*(Rd).@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Xavier
foaf_name: Goaoc, Xavier
foaf_surname: Goaoc
- foaf_Person:
foaf_givenName: Pavel
foaf_name: Paták, Pavel
foaf_surname: Paták
- foaf_Person:
foaf_givenName: Zuzana
foaf_name: Patakova, Zuzana
foaf_surname: Patakova
orcid: 0000-0002-3975-1683
- foaf_Person:
foaf_givenName: Martin
foaf_name: Tancer, Martin
foaf_surname: Tancer
orcid: 0000-0002-1191-6714
- foaf_Person:
foaf_givenName: Uli
foaf_name: Wagner, Uli
foaf_surname: Wagner
foaf_workInfoHomepage: http://www.librecat.org/personId=36690CA2-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-1494-0568
bibo_doi: 10.1007/978-3-319-44479-6_17
dct_date: 2017^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/978-331944479-6
dct_language: eng
dct_publisher: Springer@
dct_title: Bounding helly numbers via betti numbers@
...