Spanning surfaces in 3-graphs

被引：5

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

共 50 条

[31] On the Erdös–Hajnal Problem for 3-Graphs
Cherkashin D.D.
Journal of Mathematical Sciences, 2021, 255 (1) : 103 - 108
[32] Crowns in linear 3-graphs of minimum degree 4
Carbonero, Alvaro
Fletcher, Willem
Guo, Jing
Gyarfas, Andras
Wang, Rona
Yan, Shiyu
ELECTRONIC JOURNAL OF COMBINATORICS, 2022, 29 (04):
[33] Turan Numbers of Expanded Intersecting Cliques in 3-graphs
Tang, Yu-Cong
Li, Tong
Yan, Gui-Ying
JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA, 2022,
[34] On the codegree density of complete 3-graphs and related problems
Falgas-Ravry, Victor
ELECTRONIC JOURNAL OF COMBINATORICS, 2013, 20 (04):
[35] The growth rate of multicolor Ramsey numbers of 3-graphs
Bradac, Domagoj
Fox, Jacob
Sudakov, Benny
RESEARCH IN THE MATHEMATICAL SCIENCES, 2024, 11 (03)
[36] A problem of Erdős and Sós on 3-graphs
Roman Glebov
Daniel Král’
Jan Volec
Israel Journal of Mathematics, 2016, 211 : 349 - 366
[37] Optimal Orthogonal Drawings of Planar 3-Graphs in Linear Time
Didimo, Walter
Liotta, Giuseppe
Ortali, Giacomo
Patrignani, Maurizio
PROCEEDINGS OF THE 2020 ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, SODA, 2020, : 806 - 825
[38] CONSTRUCTING DENSE GRID-FREE LINEAR 3-GRAPHS
Gishboliner, Lior
Shapira, Asaf
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (01) : 69 - 74
[39] Bend-minimum orthogonal drawings of plane 3-graphs
Rahman, MS
Nishizeki, T
GRAPH-THEORETIC CONCEPTS IN COMPUTER SCIENCE, 2002, 2573 : 367 - 378
[40] Optimal Orthogonal Drawings of Planar 3-Graphs in Linear Time
Didimo, Walter
Liotta, Giuseppe
Ortali, Giacomo
Patrignani, Maurizio
PROCEEDINGS OF THE THIRTY-FIRST ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA'20), 2020, : 806 - 825

← 1 2 3 4 5 →