József Balogh

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20232026

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8 papers · 1 filter

math.CO2026

Bipartite cuts in Ramsey-Turán style

József Balogh, Ce Chen, Bernard Lidický

We prove that every $K_{5}$ -free $n$ -vertex graph with sublinear independence number can be made bipartite by removing at most $n^{2} (1/18 + o (1))$ edges, where the constant $1/18$ is be…

math.CO2026

Balanced bipartite distance of $K_{4}$ -free graphs

József Balogh, Ignacy Buczek, Andrzej Grzesik +1

We show that every $K_{4}$ -free graph on $n$ vertices can be made balanced bipartite by removing at most $\frac{n ^{2}}{9}$ edges. This proves a conjecture of Balogh, Clemen, and Lidick…

math.CO2026

Forbidding Exactly One Hamming Distance

József Balogh, Ce Chen, Bowen Li

Addressing questions raised in recent papers, we study the $r$ -distance graph $H_{r} (n)$ on the Boolean cube ${0, 1}^{n}$ , where two vertices are adjacent if their Hamming distance is…

math.CO2026

A Jump in the Codegree Turán Densities of Long Tight Cycles

József Balogh, Haoran Luo, Maya Sankar

We study the codegree Turán density of $C_{ℓ}^{r}$ , the $r$ -uniform hypergraph tight cycle of length $ℓ$ . A result of Han, Lo, and Sanhueza-Matamala states that if $\el…

math.CO2025

Maximal independent sets in the middle two layers of the Boolean lattice

József Balogh, Ce Chen, Ramon I. Garcia

Let $B (2 d - 1, d)$ be the subgraph of the hypercube $Q_{2 d - 1}$ induced by its two largest layers. Duffus, Frankl and Rödl proposed the problem of finding the asymptotics fo…

math.CO2025

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces

József Balogh, Haoran Luo

Let $α (F_{q}^{d}, p)$ be the maximum possible size of a point set in general position in the $p$ -random subset of $F_{q}^{d}$ . In this note, we determine the order of ma…

math.CO2024

On the maximum $F$ -free induced subgraphs in $K_{t}$ -free graphs

József Balogh, Ce Chen, Haoran Luo

For graphs $F$ and $H$ , let $f_{F, H} (n)$ be the minimum possible size of a maximum $F$ -free induced subgraph in an $n$ -vertex $H$ -free graph. This notion generalizes the Ramsey fun…

math.CO2023

On the Constructor-Blocker Game

József Balogh, Ce Chen, Sean English

In the Constructor-Blocker game, two players, Constructor and Blocker, alternatively claim unclaimed edges of the complete graph $K_{n}$ . For given graphs $F$ and $H$ , Constructor ca…

Bipartite cuts in Ramsey-Turán style

Balanced bipartite distance of K4​-free graphs

Forbidding Exactly One Hamming Distance

A Jump in the Codegree Turán Densities of Long Tight Cycles

Maximal independent sets in the middle two layers of the Boolean lattice

Maximum number of points in general position in a random subset of finite 3-dimensional spaces

On the maximum F-free induced subgraphs in Kt​-free graphs

On the Constructor-Blocker Game

Balanced bipartite distance of $K_{4}$ -free graphs

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces

On the maximum $F$ -free induced subgraphs in $K_{t}$ -free graphs