Amedeo Sgueglia: Spanning spheres in Dirac hypergraphs

We provide a topological extension of Dirac’s theorem and show that a k-uniform hypergraph H on n vertices has a spanning (k-1)-dimensional sphere, provided that H has no isolated vertices and each set of k-1 vertices supported by an edge is in fact supported by at least (1/2+o(1))n edges. This asymptotically confirms a conjecture of Georgakopoulos, Haslegrave, Montgomery, and Narayanan.

This is joint work with Freddie Illingworth, Richard Lang, Alp Müyesser, and Olaf Parczyk.