Spanning surfaces in 3-graphs

Agelos Georgakopoulos, John Haslegrave, Richard Montgomery, Bhargav Narayanan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 n3 C 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 n3 C o.n/contains a spanning triangulation of the sphere.

Original languageEnglish (US)
Pages (from-to)303-339
Number of pages37
JournalJournal of the European Mathematical Society
Issue number1
StatePublished - 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


  • Dirac’s theorem
  • Extremal simplicial topology
  • Spanning structures in hypergraphs
  • Triangulated surfaces


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