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...
| Κύριοι συγγραφείς: | , , , |
|---|---|
| Μορφή: | Journal article |
| Γλώσσα: | English |
| Έκδοση: |
EMS
2021
|
| Περίληψη: | 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. |
|---|