J'ozsef Balogh

collaborators

4 papers

math.CO2026

Maximizing $K_{r} + I_{r}$ in graphs with fixed edge density

József Balogh, Andrzej Grzesik, Bernard Lidický +3

For every integer $r \geq 4$ , and $ρ \in [0, 1]$ , we asymptotically determine the maximum proportion of $r$ -element sets of vertices that induce either a clique or an independent set in…

math.CO2026

Semi-Inducibility of some small graphs

József Balogh, Bernard Lidický, Dhruv Mubayi +2

Let $H$ be a fixed graph whose edges are colored red and blue and let $β \in [0, 1]$ . Let $I (H, β)$ be the (asymptotically normalized) maximum number of copies of $H$ in a large red/…

math.CO2025

Density of rainbow triangles and properly colored $K_{4}$ 's

József Balogh, Peter Bradshaw, Ramon I. Garcia +1

We establish a sharp upper bound on the number of properly $3$ -edge-colored $K_{4}$ 's in graphs with $R$ red, $G$ green and $B$ blue edges. We give a computer-free flag-algebra proof…

math.CO2025

Infinitely many groups exhibiting intermediate growth in maximal sum-free sets

József Balogh, Ramon I. Garcia, Hong Liu +1

Given an Abelian groups $G$ , denote $μ (G)$ the size of its largest sum-free subset and $f_{m a x} (G)$ the number of maximal sum-free sets in $G$ . Confirming a prediction by Liu and…

Maximizing Kr​+Ir​ in graphs with fixed edge density

Semi-Inducibility of some small graphs

Density of rainbow triangles and properly colored K4​'s

Infinitely many groups exhibiting intermediate growth in maximal sum-free sets

Maximizing $K_{r} + I_{r}$ in graphs with fixed edge density

Density of rainbow triangles and properly colored $K_{4}$ 's