15 citations · 53 across the 46 of their papers we have counts for
7 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…
On the Turán number of ordered forests
Dániel Korándi, Gábor Tardos, István Tomon +1
An ordered graph is a simple graph with a linear order on its vertex set. The corresponding Turán problem, first studied by Pach and Tardos, asks for the maximum number $\text{…
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…
Two extensions of the Erdős-Szekeres problem
Andreas F. Holmsen, Hossein Nassajian Mojarrad, János Pach +1
According to Suk's breakthrough result on the Erdos-Szekeres problem, any point set in general position in the plane, which has no elements that form the vertex set of a convex…
A Crossing Lemma for Jordan Curves
János Pach, Natan Rubin, Gábor Tardos
If two Jordan curves in the plane have precisely one point in common, and there they do not properly cross, then the common point is called a {\em touching point}. The main result…
Controlling Lipschitz functions
Andrey Kupavskii, Janos Pach, Gabor Tardos
Given any positive integers and , we say the a sequence of points in is {\em Lipschitz--controlling} if one can select suitable values $y_i…