4 papers
Many holes but no large one: maximizing -holes while forbidding -holes
Martin Andričík, Alica Dományová, Adam Džavoronok +2
We study the maximal number of empty convex -gons (-holes) determined by an -point set in the plane in general position that contains no empty convex $\ell~…
Edge-Constrained Hamiltonian Paths on a Point Set
Todor Antić, Aleksa Džuklevski, Jiří Fiala +5
Let S be a set of distinct points in general position in the Euclidean plane. A plane Hamiltonian path on S is a crossing-free geometric path such that every point of S is a vertex…
Seeing is not believing in limited visibility cops and robbers
Bojan Bašić, Alfie Davies, Aleksa Džuklevski +2
We consider the model of limited visibility Cops and Robbers, where the cops can only see within their -neighbourhood. We prove that the number of cops needed to see the robber…
Erdős-Szekeres Maker-Breaker Games
Aleksa Džuklevski, Dömötör Pálvölgyi, Alexey Pokrovskiy +3
We present new results on Maker-Breaker games arising from the Erdős-Szekeres problem in planar geometry. This classical problem asks how large a set in general position has to be…