Spanning surfaces in 3-graphs
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...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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EMS
2021
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| _version_ | 1826307908323770368 |
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| author | Georgakopoulos, A Haslegrave, J Montgomery, R Narayanan, B |
| author_facet | Georgakopoulos, A Haslegrave, J Montgomery, R Narayanan, B |
| author_sort | Georgakopoulos, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T07:10:04Z |
| format | Journal article |
| id | oxford-uuid:f7edd092-0c76-47d1-a3cc-2c31e9fb59c3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:10:04Z |
| publishDate | 2021 |
| publisher | EMS |
| record_format | dspace |
| spelling | oxford-uuid:f7edd092-0c76-47d1-a3cc-2c31e9fb59c32022-06-14T09:57:03ZSpanning surfaces in 3-graphsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f7edd092-0c76-47d1-a3cc-2c31e9fb59c3EnglishSymplectic ElementsEMS2021Georgakopoulos, AHaslegrave, JMontgomery, RNarayanan, BWe 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. |
| spellingShingle | Georgakopoulos, A Haslegrave, J Montgomery, R Narayanan, B Spanning surfaces in 3-graphs |
| title | Spanning surfaces in 3-graphs |
| title_full | Spanning surfaces in 3-graphs |
| title_fullStr | Spanning surfaces in 3-graphs |
| title_full_unstemmed | Spanning surfaces in 3-graphs |
| title_short | Spanning surfaces in 3-graphs |
| title_sort | spanning surfaces in 3 graphs |
| work_keys_str_mv | AT georgakopoulosa spanningsurfacesin3graphs AT haslegravej spanningsurfacesin3graphs AT montgomeryr spanningsurfacesin3graphs AT narayananb spanningsurfacesin3graphs |