Spanning surfaces in 3-graphs

被引：6

作者：

Georgakopoulos, Agelos ^{[1
]}

Haslegrave, John ^{[1
]}

Montgomery, Richard ^{[2
]}

Narayanan, Bhargav ^{[3
]}

机构：

[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

[2] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

[3] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2022年 / 24卷 / 01期

基金：

英国科研创新办公室; 欧洲研究理事会;

关键词：

Extremal simplicial topology; spanning structures in hypergraphs; Dirac's theorem; triangulated surfaces; THEOREM; GRAPHS;

D O I：

10.4171/JEMS/1101

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 n3 + 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 n3 + o(n) contains a spanning triangulation of the sphere.

引用

页码：303 / 339

页数：37

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