Georgakopoulos, Agelos and Haslegrave, John and Montgomery, Richard and Narayanan, Bhargav (2022) Spanning surfaces in 3-graphs. Journal of the European Mathematical Society, 24 (1). pp. 303-339. ISSN 1435-9855
Full text not available from this repository.Abstract
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 3 n +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 3 n +o(n) contains a spanning triangulation of the sphere.