15 citations · 149 across the 60 of their papers we have counts for
10 papers · 1 filter
The Crossing Tverberg Theorem
Radoslav Fulek, Bernd Gärtner, Andrey Kupavskii +2
Tverberg's theorem is one of the cornerstones of discrete geometry. It states that, given a set of at least points in , one can find a partition $X=…
Sharp bounds for the chromatic number of random Kneser graphs
Sergei Kiselev, Andrey Kupavskii
Given positive integers , the {\it Kneser graph} is a graph whose vertex set is the collection of all -element subsets of the set , with edg…
Structure and properties of large intersecting families
Andrey Kupavskii
We say that a family of -subsets of an -element set is intersecting if any two of its sets intersect. In this paper we study properties and structure of large intersecting fa…
Degree versions of theorems on intersecting families via stability
Andrey Kupavskii
The matching number of a family of subsets of an -element set is the maximum number of pairwise disjoint sets. The families with matching number are called intersecting. The…
Incompatible intersection properties
Peter Frankl, Andrey Kupavskii
Let be a family in which any three sets have non-empty intersection and any two sets have at least elements in common. The nearly best possible bou…
Optimal Bounds on the VC-dimension
Monika Csikos, Andrey Kupavskii, Nabil H. Mustafa
The VC-dimension of a set system is a way to capture its complexity and has been a key parameter studied extensively in machine learning and geometry communities. In this paper, we…