PreprintCC BY 4.0arXiv
Overlap-Helly theorems
Abstract
In this paper we introduce a generalization of Helly's theorem closely connected to Bárány-Gromov overlap theorems (also called selection lemmas). Our main result implies both the topological colorful Helly of Kalai and Meschulam and Karasev's topological centerpoint theorem. We further investigate the topological fractional Helly theorem from this overlap perspective, and show an overlap theorem for dense complexes (a continuous second selection lemma for tame maps).
Related
BibTeX
@misc{holmsen2026overlaphelly,
title = {{Overlap-Helly theorems}},
author = {Andreas F. Holmsen and Alfredo Hubard},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.10023},
eprint = {2609.10023},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10023},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Overlap-Helly theorems
AU - Andreas F. Holmsen
AU - Alfredo Hubard
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2609.10023
UR - https://arxiv.org/abs/2609.10023
AB - In this paper we introduce a generalization of Helly's theorem closely connected to Bárány-Gromov overlap theorems (also called selection lemmas). Our main result implies both the topological colorful Helly of Kalai and Meschulam and Karasev's topological centerpoint theorem. We further investigate the topological fractional Helly theorem from this overlap perspective, and show an overlap theorem for dense complexes (a continuous second selection lemma for tame maps).
ER -