J. Balogh

activity

20032024

most citedBootstrap percolation in three dimensions

105 citations · 718 across the 103 of their papers we have counts for

collaborators

Showing math.COShow all

125 papers · 1 filter

math.CO2024

On the maximum number of $r$ -cliques in graphs free of complete $r$ -partite subgraphs

József Balogh, Suyun Jiang, Haoran Luo

We estimate the maximum possible number of cliques of size $r$ in an $n$ -vertex graph free of a fixed complete $r$ -partite graph $K_{s_{1}, s_{2}, \dots, s_{r}}$ . By viewing every $r$ -c…

math.CO2024★ 1 cited

Partitioning the hypercube into smaller hypercubes

Noga Alon, Jozsef Balogh, Vladimir N. Potapov

Denote by Q_d the d-dimensional hypercube. Addressing a recent question we estimate the number of ways the vertex set of Q_d can be partitioned into vertex disjoint smaller cubes.…

math.CO2023

Almost Congruent Triangles

József Balogh, Felix Christian Clemen, Adrian Dumitrescu

Almost $50$ years ago Erdős and Purdy asked the following question: Given $n$ points in the plane, how many triangles can be approximate congruent to equilateral triangles? They po…

math.CO2023★ 1 cited

Turán density of long tight cycle minus one hyperedge

József Balogh, Haoran Luo

Denote by $C_{ℓ}^{-}$ the $3$ -uniform hypergraph obtained by removing one hyperedge from the tight cycle on $ℓ$ vertices. It is conjectured that the Turán density of…

math.CO2023★ 2 cited

Weighted Turán theorems with applications to Ramsey-Turán type of problems

József Balogh, Domagoj Bradač, Bernard Lidický

We study extensions of Turán Theorem in edge-weighted settings. A particular case of interest is when constraints on the weight of an edge come from the order of the largest clique…

math.CO2022

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 $α > 0$ , there exists a constant $C$ such…

math.CO2022

On the sizes of $t$ -intersecting $k$ -chain-free families

József Balogh, William B. Linz, Balázs Patkós

A set system $F$ is $t$ -\textit{intersecting}, if the size of the intersection of every pair of its elements has size at least $t$ . A set system $F$ is $k$ -\tex…

math.CO2022

Nearly all $k$ -SAT functions are unate

József Balogh, Dingding Dong, Bernard Lidický +2

We prove that $1 - o (1)$ fraction of all $k$ -SAT functions on $n$ Boolean variables are unate (i.e., monotone after first negating some variables), for any fixed positive integer $k$ …

math.CO2022

New Lower Bounds For Essential Covers Of The Cube

Igor Araujo, József Balogh, Letícia Mattos

An essential cover of the vertices of the $n$ -cube ${0, 1}^{n}$ by hyperplanes is a minimal covering where no hyperplane is redundant and every variable appears in the equation of a…

math.CO2022

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 $m$ of vertices and number $f$ of edges. Extending the…

math.CO2022★ 1 cited

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

József Balogh, Felix Christian Clemen, Haoran Luo

For every integer $t \geq 0$ , denote by $F_{5}^{t}$ the hypergraph on vertex set ${1, 2, \dots, 5 + t}$ with hyperedges ${123, 124} \cup {34 k : 5 \leq k \leq 5 + t}$ . We determine $\mathr…

math.CO2022★ 1 cited

Ramsey-Turán Problems with small independence numbers

József Balogh, Ce Chen, Grace McCourt +1

Given a graph $H$ and a function $f (n)$ , the Ramsey-Turán number $R T (n, H, f (n))$ is the maximum number of edges in an $n$ -vertex $H$ -free graph with independence number at most $f(n…

math.CO2022

Maximal 3-wise Intersecting Families with Minimum Size: the Odd Case

József Balogh, Ce Chen, Haoran Luo

A family $F$ on ground set ${1, 2, \dots, n}$ is maximal $k$ -wise intersecting if every collection of $k$ sets in $F$ has non-empty intersection, and no other…

math.CO2022★ 1 cited

A sharp threshold for a random version of Sperner's Theorem

József Balogh, Robert A. Krueger

The Boolean lattice $P (n)$ consists of all subsets of $[n] = {1, \dots, n}$ partially ordered under the containment relation. Sperner's Theorem states that the largest a…

math.CO2022★ 4 cited

The Spectrum of Triangle-free Graphs

József Balogh, Felix Christian Clemen, Bernard Lidický +2

Denote by $q_{n} (G)$ the smallest eigenvalue of the signless Laplacian matrix of an $n$ -vertex graph $G$ . Brandt conjectured in 1997 that for regular triangle-free graphs $q_n(G) \le…

math.CO2022

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…

math.CO2022

On the Maximum $F_{5}$ -free Subhypergraphs of a Random Hypergraph

Igor Araujo, József Balogh, Haoran Luo

Denote by $F_{5}$ the $3$ -uniform hypergraph on vertex set ${1, 2, 3, 4, 5}$ with hyperedges ${123, 124, 345}$ . Balogh, Butterfield, Hu, and Lenz proved that if $p > K lo g n / n$ for…

math.CO2021

Rainbow connectivity of randomly perturbed graphs

József Balogh, John Finlay, Cory Palmer

In this note we examine the following random graph model: for an arbitrary graph $H$ , with quadratic many edges, construct a graph $G$ by randomly adding $m$ edges to $H$ and rando…

math.CO2021

Proper elements of Coxeter groups

József Balogh, David Brewster, Reuven Hodges

We extend the notion of proper elements to all Coxeter groups. For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to z…

math.CO2021★ 1 cited

Maximal $3$ -wise intersecting families

József Balogh, Ce Chen, Kevin Hendrey +4

A family $F$ on ground set $[n] := {1, 2, \dots, n}$ is maximal $k$ -wise intersecting if every collection of at most $k$ sets in $F$ has non-empty intersection,…

math.CO2021★ 11 cited

Solving Turán's Tetrahedron Problem for the $ℓ_{2}$ -Norm

József Balogh, Felix Christian Clemen, Bernard Lidický

Turán's famous tetrahedron problem is to compute the Turán density of the tetrahedron $K_{4}^{3}$ . This is equivalent to determining the maximum $ℓ_{1}$ -norm of the codegree vector of…

math.CO2021★ 1 cited

Hypergraph Turán Problems in $ℓ_{2}$ -Norm

József Balogh, Felix Christian Clemen, Bernard Lidický

There are various different notions measuring extremality of hypergraphs. In this survey we compare the recently introduced notion of the codegree squared extremal function with th…

math.CO2021

On generalized Turán results in height two posets

József Balogh, Ryan R. Martin, Dániel T. Nagy +1

For given posets $P$ and $Q$ and an integer $n$ , the generalized Turán problem for posets, asks for the maximum number of copies of $Q$ in a $P$ -free subset of the $n$ -dimensional…

math.CO2021

Counting $r$ -graphs without forbidden configurations

József Balogh, Felix Christian Clemen, Letícia Mattos

One of the major problems in combinatorics is to determine the number of $r$ -uniform hypergraphs ( $r$ -graphs) on $n$ vertices which are free of certain forbidden structures. This p…

On the maximum number of r-cliques in graphs free of complete r-partite subgraphs

Partitioning the hypercube into smaller hypercubes

Almost Congruent Triangles

Turán density of long tight cycle minus one hyperedge

Weighted Turán theorems with applications to Ramsey-Turán type of problems

On oriented cycles in randomly perturbed digraphs

On the sizes of t-intersecting k-chain-free families

Nearly all k-SAT functions are unate

New Lower Bounds For Essential Covers Of The Cube

Unavoidable order-size pairs in hypergraphs -- positive forcing density

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

Ramsey-Turán Problems with small independence numbers

Maximal 3-wise Intersecting Families with Minimum Size: the Odd Case

A sharp threshold for a random version of Sperner's Theorem

The Spectrum of Triangle-free Graphs

10 Problems for Partitions of Triangle-free Graphs

On the Maximum F5​-free Subhypergraphs of a Random Hypergraph

Rainbow connectivity of randomly perturbed graphs

Proper elements of Coxeter groups

Maximal 3-wise intersecting families

Solving Turán's Tetrahedron Problem for the ℓ2​-Norm

Hypergraph Turán Problems in ℓ2​-Norm

On generalized Turán results in height two posets

Counting r-graphs without forbidden configurations

On the maximum number of $r$ -cliques in graphs free of complete $r$ -partite subgraphs

On the sizes of $t$ -intersecting $k$ -chain-free families

Nearly all $k$ -SAT functions are unate

On the Maximum $F_{5}$ -free Subhypergraphs of a Random Hypergraph

Maximal $3$ -wise intersecting families

Solving Turán's Tetrahedron Problem for the $ℓ_{2}$ -Norm

Hypergraph Turán Problems in $ℓ_{2}$ -Norm

Counting $r$ -graphs without forbidden configurations