4 papers
Hyperfiniteness on Topological Ramsey Spaces
Balázs Bursics, Zoltán Vidnyánszky
We investigate the behavior of countable Borel equivalence relations (CBERs) on topological Ramsey spaces. First, we give a simple proof of the fact that every CBER on $[\mathbb{N}…
Hitting sets and colorings of hypergraphs
Balázs Bursics, Bence Csonka, Luca Szepessy
In this paper we study the minimal size of edges in hypergraph families that guarantees the existence of a polychromatic coloring, that is, a -coloring of a vertex set such that…
A coloring of the plane without monochromatic right triangles
Balázs Bursics, Péter Komjáth
We give a full, correct proof of the following result, earlier claimed by Erdős and Komjáth. If the Continuum Hypothesis holds then there is a coloring of the plane with countably…
Avoiding right angles and certain Hamming distances
Balázs Bursics, Dávid Matolcsi, Péter Pál Pach +1
In this paper we show that the largest possible size of a subset of avoiding right angles, that is, distinct vectors such that and are perpendi…