105 citations · 718 across the 103 of their papers we have counts for
12 papers · 2 filters
On oriented cycles in randomly perturbed digraphs
Igor Araujo, József Balogh, Robert A. Krueger +2
In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every , there exists a constant such…
On the sizes of -intersecting -chain-free families
József Balogh, William B. Linz, Balázs Patkós
A set system is -\textit{intersecting}, if the size of the intersection of every pair of its elements has size at least . A set system is -\tex…
Nearly all -SAT functions are unate
József Balogh, Dingding Dong, Bernard Lidický +2
We prove that fraction of all -SAT functions on Boolean variables are unate (i.e., monotone after first negating some variables), for any fixed positive integer …
New Lower Bounds For Essential Covers Of The Cube
Igor Araujo, József Balogh, Letícia Mattos
An essential cover of the vertices of the -cube by hyperplanes is a minimal covering where no hyperplane is redundant and every variable appears in the equation of a…
Unavoidable order-size pairs in hypergraphs -- positive forcing density
Maria Axenovich, József Balogh, Felix Christian Clemen +1
Erdős, Füredi, Rothschild and Sós initiated a study of classes of graphs that forbid every induced subgraph on a given number of vertices and number of edges. Extending the…
Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions
József Balogh, Felix Christian Clemen, Haoran Luo
For every integer , denote by the hypergraph on vertex set with hyperedges . We determine $\mathr…
Ramsey-Turán Problems with small independence numbers
József Balogh, Ce Chen, Grace McCourt +1
Given a graph and a function , the Ramsey-Turán number is the maximum number of edges in an -vertex -free graph with independence number at most $f(n…
Maximal 3-wise Intersecting Families with Minimum Size: the Odd Case
József Balogh, Ce Chen, Haoran Luo
A family on ground set is maximal -wise intersecting if every collection of sets in has non-empty intersection, and no other…
A sharp threshold for a random version of Sperner's Theorem
József Balogh, Robert A. Krueger
The Boolean lattice consists of all subsets of partially ordered under the containment relation. Sperner's Theorem states that the largest a…
The Spectrum of Triangle-free Graphs
József Balogh, Felix Christian Clemen, Bernard Lidický +2
Denote by the smallest eigenvalue of the signless Laplacian matrix of an -vertex graph . Brandt conjectured in 1997 that for regular triangle-free graphs $q_n(G) \le…
10 Problems for Partitions of Triangle-free Graphs
József Balogh, Felix Christian Clemen, Bernard Lidický
We will state 10 problems, and solve some of them, for partitions in triangle-free graphs related to Erdős' Sparse Half Conjecture. Among others we prove the following variant of i…
On the Maximum -free Subhypergraphs of a Random Hypergraph
Igor Araujo, József Balogh, Haoran Luo
Denote by the -uniform hypergraph on vertex set with hyperedges . Balogh, Butterfield, Hu, and Lenz proved that if for…