104 citations · 132 across the 9 of their papers we have counts for
5 papers · 2 filters
Large subgraphs in rainbow-triangle free colorings
Adam Zsolt Wagner
Fox--Grinshpun--Pach showed that every -coloring of the complete graph on vertices without a rainbow triangle contains a clique of size which…
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\…
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-…