Aleksa Dzuklevski

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math.CO2026

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

Martin AndriÄÃk, Alica DomÃ¡nyovÃ¡, Adam DÅ¾avoronok +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

ErdÅs-Szekeres Maker-Breaker Games

Aleksa DÅ¾uklevski, DÃ¶mÃ¶tÃ¶r PÃ¡lvÃ¶lgyi, Alexey Pokrovskiy +3

We present new results on Maker-Breaker games arising from the ErdÅs-Szekeres problem in planar geometry. This classical problem asks how large a set in general position has to be…

math.CO2025

Seeing is not believing in limited visibility cops and robbers

Bojan BaÅ¡iÄ, Alfie Davies, Aleksa DÅ¾uklevski +2

We consider the model of limited visibility Cops and Robbers, where the cops can only see within their $l$ -neighbourhood. We prove that the number of cops needed to see the robber…

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

ErdÅs-Szekeres Maker-Breaker Games

Seeing is not believing in limited visibility cops and robbers

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

ErdÅs-Szekeres Maker-Breaker Games