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Georgakopoulos, Agelos, Haslegrave, John, Montgomery, Richard and Narayanan, Bhargav (2021) Spanning surfaces in 3-graphs. Journal of the European Mathematical Society, 24 (1). pp. 303-339. doi:10.4171/JEMS/1101 ISSN 1435-9855.
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Official URL: https://doi.org/10.4171/JEMS/1101
Abstract
We prove a topological extension of Dirac's theorem suggested by Gowers in 2005: for any connected, closed surface \mathscr{S}S, we show that any two-dimensional simplicial complex on nn vertices in which each pair of vertices belongs to at least \frac n3 + o(n) 3nā +o(n) facets contains a homeomorph of \mathscr{S}S spanning all the vertices. This result is asymptotically sharp, and implies in particular that any 3-uniform hypergraph on nn vertices with minimum codegree exceeding \frac n3+o(n) 3nā +o(n) contains a spanning triangulation of the sphere.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Hypergraphs, Surfaces , Hamiltonian systems | |||||||||
| Journal or Publication Title: | Journal of the European Mathematical Society | |||||||||
| Publisher: | European Mathematical Society Publishing House | |||||||||
| ISSN: | 1435-9855 | |||||||||
| Official Date: | 25 August 2021 | |||||||||
| Dates: |
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| Volume: | 24 | |||||||||
| Number: | 1 | |||||||||
| Page Range: | pp. 303-339 | |||||||||
| DOI: | 10.4171/JEMS/1101 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 28 July 2021 | |||||||||
| Date of first compliant Open Access: | 28 July 2021 | |||||||||
| RIOXX Funder/Project Grant: |
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