158 research outputs found
Spanning surfaces in 3-graphs
We prove a topological extension of Dirac's theorem suggested by Gowers in
2005: for any connected, closed surface , we show that any
two-dimensional simplicial complex on vertices in which each pair of
vertices belongs to at least facets contains a homeomorph of
spanning all the vertices. This result is asymptotically sharp,
and implies in particular that any 3-uniform hypergraph on vertices with
minimum codegree exceeding contains a spanning triangulation of the
-sphere.Comment: 33 pages, 6 figure
- …