Helly type problems in convexity spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910832295673856 |
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| author | Holmsen, Andreas F. |
| author_facet | Holmsen, Andreas F. |
| contents | 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 $\varepsilon$-nets, and $(p,q)$-theorems. As an application of the theory of convexity spaces we introduce new classes of uniform hypergraphs and show that they are $χ$-bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Helly type problems in convexity spaces Holmsen, Andreas F. Combinatorics 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 $\varepsilon$-nets, and $(p,q)$-theorems. As an application of the theory of convexity spaces we introduce new classes of uniform hypergraphs and show that they are $χ$-bounded. |
| title | Helly type problems in convexity spaces |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.05871 |