Spanning surfaces in 3-graphs

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

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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.

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Journal Article
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Journal of the European Mathematical Society
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17 May 2024 15:35
Last Modified:
20 Jun 2024 09:35