105 citations · 718 across the 103 of their papers we have counts for
10 papers · 2 filters
Kleitman's conjecture about families of given size minimizing the number of -chains
Jozsef Balogh, Adam Zsolt Wagner
A central theorem in combinatorics is Sperner's Theorem, which determines the maximum size of a family that does not contain a -chain $F_1\…
Transference for the Erdős-Ko-Rado theorem
József Balogh, Béla Bollobás, Bhargav Narayanan
For natural numbers with , the Kneser graph is the graph on the family of -element subsets of in which two sets are adjacen…
Triangle-tilings in graphs without large independent sets
József Balogh, Andrew McDowell, Theodore Molla +1
We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an -vertex graph with sublinear independence number. In th…
On two problems in Ramsey-Turán theory
József Balogh, Hong Liu, Maryam Sharifzadeh
Alon, Balogh, Keevash and Sudakov proved that the -partite Turán graph maximizes the number of distinct -edge-colorings with no monochromatic for all fixed and…
Edit distance and its computation
József Balogh, Ryan R. Martin
In this paper, we provide a method for determining the asymptotic value of the maximum edit distance from a given hereditary property. This method permits the edit distance to be c…
The diameter game
József Balogh, Ryan R. Martin, András Pluhár
A large class of Positional Games are defined on the complete graph on vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his su…
The number of subsets of integers with no -term arithmetic progression
József Balogh, Hong Liu, Maryam Sharifzadeh
Addressing a question of Cameron and Erd\Ho s, we show that, for infinitely many values of , the number of subsets of that do not contain a -term arithmet…
Applications of graph containers in the Boolean lattice
Jozsef Balogh, Andrew Treglown, Adam Zsolt Wagner
We apply the graph container method to prove a number of counting results for the Boolean lattice . In particular, we: (i) Give a partial answer to a question of Sap…
Further applications of the Container Method
Jozsef Balogh, Adam Zsolt Wagner
Recently, Balogh--Morris--Samotij and Saxton--Thomason proved that hypergraphs satisfying some natural conditions have only few independent sets. Their main results already have se…
On the number of union-free families
Jozsef Balogh, Adam Zsolt Wagner
A family of sets is union-free if there are no three distinct sets in the family such that the union of two of the sets is equal to the third set. Kleitman proved that every union-…