48 citations · 165 across the 65 of their papers we have counts for
10 papers · 2 filters
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…
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…
Erdos-Hajnal conjecture for graphs with bounded VC-dimension
Jacob Fox, János Pach, Andrew Suk
The Vapnik-Chervonenkis dimension (in short, VC-dimension) of a graph is defined as the VC-dimension of the set system induced by the neighborhoods of its vertices. We show that ev…
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…
Thrackles: An Improved Upper Bound
Radoslav Fulek, János Pach
A {\em thrackle} is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle…
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…