Spanning surfaces in 3-graphs

We prove a topological extension of Dirac's theorem suggested by Gowers in 2005: for any connected, closed surface S, we show that any two-dimensional simplicial complex on n vertices in which each pair of vertices belongs to at least n/3+o(n) facets contains a homeomorph of S spanning all the...

Szczegółowa specyfikacja

Opis bibliograficzny
Główni autorzy: Georgakopoulos, A, Haslegrave, J, Montgomery, R, Narayanan, B
Format: Journal article
Język:English
Wydane: EMS 2021
Opis
Streszczenie:We prove a topological extension of Dirac's theorem suggested by Gowers in 2005: for any connected, closed surface S, we show that any two-dimensional simplicial complex on n vertices in which each pair of vertices belongs to at least n/3+o(n) facets contains a homeomorph of S spanning all the vertices. This result is asymptotically sharp, and implies in particular that any 3-uniform hypergraph on n vertices with minimum codegree exceeding n/3+o(n) contains a spanning triangulation of the sphere.