English

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 ε\varepsilon-nets, and (p,q)(p,q)-theorems. As an application of the theory of convexity spaces we introduce new classes of uniform hypergraphs and show that they are χ\chi-bounded.

Keywords

Cite

@article{arxiv.2408.05871,
  title  = {Helly type problems in convexity spaces},
  author = {Andreas F. Holmsen},
  journal= {arXiv preprint arXiv:2408.05871},
  year   = {2025}
}
R2 v1 2026-06-28T18:09:58.810Z