Helly type problems in convexity spaces
Combinatorics
2025-02-18 v4
Abstract
We report on some recent progress regarding combinatorial properties in convexity spaces with a bounded Radon number. In particular, we discuss the relationship between the Radon number, the colorful and fractional Helly properties, weak -nets, and -theorems. As an application of the theory of convexity spaces we introduce new classes of uniform hypergraphs and show that they are -bounded.
Cite
@article{arxiv.2408.05871,
title = {Helly type problems in convexity spaces},
author = {Andreas F. Holmsen},
journal= {arXiv preprint arXiv:2408.05871},
year = {2025}
}