یادداشتی بر قضیه هلی کسری رنگین
abstract
Helly’s theorem is a classical result concerning the intersection patterns of convex sets in R d . Two important generalizations are the colorful version and the fractional version. Recently, Bárány et al. combined the two, obtaining a colorful fractional Helly theorem. In this paper, we give an improved version of their result.
1. Introduction
Helly’s theorem is one of the most well-known and fundamental results in combinatorial geometry, which has various generalizations and applications. It was first proved by Helly [12] in 1913, but his proof was not published until 1923, after alternative proofs by Radon [17] and König [15]. We recommend the survey paper by Amenta, Loera, and Soberón [4] for an overview of previous results and open problems related to Helly’s theorem. Recall that a family is intersecting if the intersection of all members is non-empty. The following is the original version of Helly’s theorem.
چکیده
1.مقدمه
2. اثبات از قضیه 1.6
2.1 عدد تطابق از ابرگراف ها
2.2. اثبات از قضیه 1.6
3. کران بالا
4. تذکرها
abstract
1. Introduction
2. Proof of Theorem 1.6
2.1. The matching number of hypergraphs
2.2. Proof of Theorem 1.6
3. The upper bound
4. Remarks
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