1. Spanning surfaces in 3-graphs.
- Author
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Georgakopoulos, Agelos, Haslegrave, John, Montgomery, Richard, and Narayanan, Bhargav
- Subjects
- *
GRAPH theory , *HYPERGRAPHS , *DIRAC function , *HOMEOMORPHISMS , *GEOMETRIC vertices - 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 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. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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