105 citations · 718 across the 103 of their papers we have counts for
10 papers · 1 filter
An efficient container lemma
József Balogh, Wojciech Samotij
We prove a new, efficient version of the hypergraph container theorems that is suited for hypergraphs with large uniformities. The main novelty is a refined approach to constructin…
Making -Free Graphs -partite
József Balogh, Felix Christian Clemen, Mikhail Lavrov +2
The Erdős-Simonovits stability theorem states that for all ε>0 there exists α>0 such that if G is a K_{r+1}-free graph on n vertices with e(G) > ex(n,K_{r+1}) - αn^2, then one can…
An analogue of the Erdős-Gallai theorem for random graphs
József Balogh, Andrzej Dudek, Lina Li
Recently, variants of many classical extremal theorems have been proved in the random environment. We, complementing existing results, extend the Erdős-Gallai Theorem in random gra…
The maximum length of -Bootstrap Percolation
József Balogh, Gal Kronenberg, Alexey Pokrovskiy +1
Graph-bootstrap percolation, also known as weak saturation, was introduced by Bollobás in 1968. In this process, we start with initial "infected" set of edges , and we infect…
Monochromatic paths and cycles in -edge-colored graphs with large minimum degree
József Balogh, Alexandr Kostochka, Mikhail Lavrov +1
A graph arrows a graph if in every -edge-coloring of there exists a monochromatic copy of . Schelp had the idea that if the complete graph arrows a small gr…
Long monochromatic paths and cycles in 2-edge-colored multipartite graphs
József Balogh, Alexandr Kostochka, Mikhail Lavrov +1
We solve four similar problems: For every fixed and large , we describe all values of such that for every -edge-coloring of the complete -partite grap…