Adam Džavoronok

collaborators

4 papers

math.CO2026

Supersaturation of induced even cycles in locally sparse graphs

Adam Džavoronok, Ole Gabsdil, Alexander Mylet +2

A graph $Γ$ is $(c, t)$ -sparse for $c > 0$ and $t \geq 1$ if for every pair of vertex subsets $A, B \subseteq V (Γ)$ with $∣ A ∣, ∣ B ∣ \geq t$ , the number of edges $e (A, B)$ between them s…

math.CO2026

Venn diagrams as forbidden hypergraph traces

Adam Džavoronok, Tymofii Reizin, Jakub Šošovička

We study the maximum size of a set system that contains no $k$ -Venn diagram, denoted by $V D_{k}$ , as a trace. For every fixed $k \geq 3$ , we prove $\text{ex}_{tr}(n,VD_k)=O_k(n^{2^k-2k…

math.CO2026

Many holes but no large one: maximizing $k$ -holes while forbidding $(k + 1)$ -holes

Martin Andričík, Alica Dományová, Adam Džavoronok +2

We study the maximal number $m_{k, ℓ, n}$ of empty convex $k$ -gons ( $k$ -holes) determined by an $n$ -point set in the plane in general position that contains no empty convex $\ell~…

math.CO2026

Monochromatic Paths and a Topological Approach to Norine's Conjecture

Adam Džavoronok

Motivated by Norine's conjecture, this paper investigates monochromatic antipodal paths in $2$ -edge-coloured hypercubes and simplicial complexes. Our main method relies on a topolo…

Supersaturation of induced even cycles in locally sparse graphs

Venn diagrams as forbidden hypergraph traces

Many holes but no large one: maximizing k-holes while forbidding (k+1)-holes

Monochromatic Paths and a Topological Approach to Norine's Conjecture

Many holes but no large one: maximizing $k$ -holes while forbidding $(k + 1)$ -holes