48 citations · 165 across the 65 of their papers we have counts for
5 papers · 2 filters
Decomposition of a cube into nearly equal smaller cubes
Peter Frankl, Amram Meir, Janos Pach
Let be a fixed positive integer and let . It is shown that for every sufficiently large , the -dimensional unit cube can be decomposed into exactly …
Separation with restricted families of sets
Zsolt Lángi, Márton Naszódi, János Pach +2
Given a finite -element set , a family of subsets is said to separate if any two elements of are separated by at least one member of $\mathc…
Semi-algebraic colorings of complete graphs
Jacob Fox, Janos Pach, Andrew Suk
We consider -colorings of the edges of a complete graph, where each color class is defined semi-algebraically with bounded complexity. The case was first studied by Alon…
Beyond the Richter-Thomassen Conjecture
János Pach, Natan Rubin, Gábor Tardos
If two closed Jordan curves in the plane have precisely one point in common, then it is called a {\em touching point}. All other intersection points are called {\em crossing points…
A polynomial regularity lemma for semi-algebraic hypergraphs and its applications in geometry and property testing
Jacob Fox, Janos Pach, Andrew Suk
Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic -uniform hypergraphs of bounded complexity, showing that for each the vertex set can be…