Olaf Parczyk

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20242026

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3 papers · 1 filter

math.CO2025

The maximum diameter of 2-dimensional simplicial complexes

Olaf Parczyk, Silas Rathke, Tibor SzabÃ³

We study a problem of Santos about the largest possible diameter of a $d$ -dimensional (abstract) simplicial complex on $n$ vertices. For dimension 2, we determine the exact value o…

math.CO2025

Spanning spheres in Dirac hypergraphs

Freddie Illingworth, Richard Lang, Alp MÃ¼yesser +2

We show that a $k$ -uniform hypergraph on $n$ vertices has a spanning subgraph homeomorphic to the $(k - 1)$ -dimensional sphere provided that $H$ has no isolated vertices and each s…

math.CO2025

On product Schur triples in the integers

LetÃcia Mattos, Domenico Mergoni Cecchelli, Olaf Parczyk

Schur's theorem states that in any $k$ -colouring of the set of integers $[n]$ there is a monochromatic solution to $a + b = c$ , provided $n$ is sufficiently large. Abbott and Wang stud…