15 citations · 149 across the 60 of their papers we have counts for
14 papers · 1 filter
Tilings of the plane with unit area triangles of bounded diameter
Andrey Kupavskii, János Pach, Gábor Tardos
There exist tilings of the plane with pairwise noncongruent triangles of equal area and bounded perimeter. Analogously, there exist tilings with triangles of equal perimeter, the a…
When are epsilon-nets small?
Andrey Kupavskii, Nikita Zhivotovskiy
In many interesting situations the size of epsilon-nets depends only on together with different complexity measures. The aim of this paper is to give a systematic treatment of…
Tilings with noncongruent triangles
Andrey Kupavskii, János Pach, Gábor Tardos
We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that no con…
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 different extremal properties of intersecting fa…
Regular Intersecting Families
Ferdinand Ihringer, Andrey Kupavskii
We call a family of sets intersecting, if any two sets in the family intersect. In this paper we investigate intersecting families of -element subsets of $[n]:=\{1…
Diversity of uniform intersecting families
Andrey Kupavskii
A family is called intersecting if any two of its sets intersect. Given an intersecting family, its diversity is the number of sets not passing through…