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The maximum diameter of -dimensional simplicial complexes
Stefan Glock, Olaf Parczyk, Silas Rathke +1
For every fixed dimension and sufficiently large , we determine the maximum possible diameter of a strongly connected -dimensional simplicial complex on vertices. Thi…
The maximum diameter of 2-dimensional simplicial complexes
Olaf Parczyk, Silas Rathke, Tibor Szabó
We study a problem of Santos about the largest possible diameter of a -dimensional (abstract) simplicial complex on vertices. For dimension 2, we determine the exact value o…
Adjunctions, Box Products, and Forcing Families
Aldo Kiem, Olaf Parczyk, Christoph Spiegel
Sidorenko's conjecture states that the number of copies of any given bipartite graph in another graph of given density is asymptotically minimized by a random graph. For bipartite…
An Unsure Note on an Un-Schur Problem
Olaf Parczyk, Christoph Spiegel
Graham, Rödl, and Ruciński originally posed the problem of determining the minimum number of monochromatic Schur triples that must appear in any 2-coloring of the first integer…
Dirac's theorem for graphs of bounded bandwidth
Alberto Espuny Díaz, Pranshu Gupta, Domenico Mergoni Cecchelli +2
We provide an optimal sufficient condition, relating minimum degree and bandwidth, for a graph to contain a spanning subdivision of the complete bipartite graph . This…
Spanning spheres in Dirac hypergraphs
Freddie Illingworth, Richard Lang, Alp Müyesser +2
We show that a -uniform hypergraph on vertices has a spanning subgraph homeomorphic to the -dimensional sphere provided that has no isolated vertices and each s…
On product Schur triples in the integers
Letícia Mattos, Domenico Mergoni Cecchelli, Olaf Parczyk
Schur's theorem states that in any -colouring of the set of integers there is a monochromatic solution to , provided is sufficiently large. Abbott and Wang stud…