Intersection patterns of planar sets

G. Kalai, Z. Patakova, Discrete and Computational Geometry (2020).


Journal Article | Epub ahead of print | English

Scopus indexed
Author
Department
Abstract
Let A={A1,…,An} be a family of sets in the plane. For 0≤i<n, denote by fi the number of subsets σ of {1,…,n} of cardinality i+1 that satisfy ⋂i∈σAi≠∅. Let k≥2 be an integer. We prove that if each k-wise and (k+1)-wise intersection of sets from A is empty, or a single point, or both open and path-connected, then fk+1=0 implies fk≤cfk−1 for some positive constant c depending only on k. Similarly, let b≥2, k>2b be integers. We prove that if each k-wise or (k+1)-wise intersection of sets from A has at most b path-connected components, which all are open, then fk+1=0 implies fk≤cfk−1 for some positive constant c depending only on b and k. These results also extend to two-dimensional compact surfaces.
Publishing Year
Date Published
2020-06-02
Journal Title
Discrete and Computational Geometry
ISSN
eISSN
IST-REx-ID

Cite this

Kalai G, Patakova Z. Intersection patterns of planar sets. Discrete and Computational Geometry. 2020. doi:10.1007/s00454-020-00205-z
Kalai, G., & Patakova, Z. (2020). Intersection patterns of planar sets. Discrete and Computational Geometry. https://doi.org/10.1007/s00454-020-00205-z
Kalai, Gil, and Zuzana Patakova. “Intersection Patterns of Planar Sets.” Discrete and Computational Geometry, 2020. https://doi.org/10.1007/s00454-020-00205-z.
G. Kalai and Z. Patakova, “Intersection patterns of planar sets,” Discrete and Computational Geometry, 2020.
Kalai G, Patakova Z. 2020. Intersection patterns of planar sets. Discrete and Computational Geometry.
Kalai, Gil, and Zuzana Patakova. “Intersection Patterns of Planar Sets.” Discrete and Computational Geometry, Springer Nature, 2020, doi:10.1007/s00454-020-00205-z.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 1907.00885

Search this title in

Google Scholar