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Quantitative Fractional Helly and (p,q)-Theorems
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2021-09-03 , DOI: 10.1016/j.ejc.2021.103424 Attila Jung 1 , Márton Naszódi 2, 3
中文翻译:
定量分数 Helly 和 (p,q) - 定理
更新日期:2021-09-04
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2021-09-03 , DOI: 10.1016/j.ejc.2021.103424 Attila Jung 1 , Márton Naszódi 2, 3
Affiliation
We consider quantitative versions of Helly-type questions, that is, instead of finding a point in the intersection, we bound the volume of the intersection. Our first main result is a quantitative version of the Fractional Helly Theorem of Katchalski and Liu, the second one is a quantitative version of the -Theorem of Alon and Kleitman.
中文翻译:
定量分数 Helly 和 (p,q) - 定理
我们考虑 Helly 类型问题的定量版本,也就是说,我们不是在交叉点中找到一个点,而是限制了交叉点的体积。我们的第一个主要结果是 Katchalski 和 Liu 分数 Helly 定理的定量版本,第二个是 -阿隆和克莱特曼的定理。