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...
| প্রধান লেখক: | , , , |
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| বিন্যাস: | Journal article |
| ভাষা: | English |
| প্রকাশিত: |
EMS
2021
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| সংক্ষিপ্ত: | 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. |
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