Andrzej Grzesik

activity

20182026

most citedThe Turán number of blow-ups of trees

2 citations · 2 across the 11 of their papers we have counts for

collaborators

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19 papers · 1 filter

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

Rainbow Turán numbers for paths of length four

Sylwia Antoniuk, Andrzej Grzesik, Magdalena Prorok +1

Given a set $V$ of $n$ vertices and an integer $k \geq 1$ , our goal is to maximize the number of edges in graphs $G_{1}, G_{2}, \dots, G_{k}$ , defined on $V$ , under the constraint that the…

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.CO2025

Cycle lengths in graphs of given minimum degree

Yandong Bai, Andrzej Grzesik, Binlong Li +1

We prove that if $G$ is a 2-connected graph with minimum degree at least $k ⩾ 4$ , then (1) $G$ contains $k$ cycles whose lengths form an arithmetic progression with common d…

math.CO2025

Antidirected paths in oriented graphs

Andrzej Grzesik, Marek Skrzypczyk

We show that for any integer $k \geq 4$ , every oriented graph with minimum semidegree bigger than $\frac{1}{2} (k - 1 + k - 3)$ contains an antidirected path of length $k$ . Conseque…

math.CO2025

Generalized Turán problem for directed cycles

Andrzej Grzesik, Justyna Jaworska, Bartłomiej Kielak +2

For integers $k, ℓ \geq 3$ , let $ex (n, C_{k}, C_{ℓ})$ denote the maximum number of directed cycles of length $k$ in any oriented graph…

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

Rainbow Turán numbers for paths of length four

Balanced bipartite distance of K4​-free graphs

Cycle lengths in graphs of given minimum degree

Antidirected paths in oriented graphs

Generalized Turán problem for directed cycles

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

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