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Spanning surfaces in 3-graphs.
- Source :
-
Journal of the European Mathematical Society (EMS Publishing) . 2022, Vol. 24 Issue 1, p303-339. 37p. - Publication Year :
- 2022
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GRAPH theory
*HYPERGRAPHS
*DIRAC function
*HOMEOMORPHISMS
*GEOMETRIC vertices
Subjects
Details
- Language :
- English
- ISSN :
- 14359855
- Volume :
- 24
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of the European Mathematical Society (EMS Publishing)
- Publication Type :
- Academic Journal
- Accession number :
- 157511734
- Full Text :
- https://doi.org/10.4171/JEMS/1101