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Spanning surfaces in 3-graphs

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Spanning surfaces in 3-graphs. / Georgakopoulos, Agelos; Haslegrave, John; Montgomery, Richard et al.
In: Journal of the European Mathematical Society, Vol. 24, No. 1, 31.03.2022, p. 303-339.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Georgakopoulos, A, Haslegrave, J, Montgomery, R & Narayanan, B 2022, 'Spanning surfaces in 3-graphs', Journal of the European Mathematical Society, vol. 24, no. 1, pp. 303-339. https://doi.org/10.4171/JEMS/1101

APA

Georgakopoulos, A., Haslegrave, J., Montgomery, R., & Narayanan, B. (2022). Spanning surfaces in 3-graphs. Journal of the European Mathematical Society, 24(1), 303-339. https://doi.org/10.4171/JEMS/1101

Vancouver

Georgakopoulos A, Haslegrave J, Montgomery R, Narayanan B. Spanning surfaces in 3-graphs. Journal of the European Mathematical Society. 2022 Mar 31;24(1):303-339. Epub 2021 Aug 25. doi: 10.4171/JEMS/1101

Author

Georgakopoulos, Agelos ; Haslegrave, John ; Montgomery, Richard et al. / Spanning surfaces in 3-graphs. In: Journal of the European Mathematical Society. 2022 ; Vol. 24, No. 1. pp. 303-339.

Bibtex

@article{9a99244fd7b04ab086d305c26621ef52,
title = "Spanning surfaces in 3-graphs",
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 3n​ +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 3n​ +o(n) contains a spanning triangulation of the sphere.",
author = "Agelos Georgakopoulos and John Haslegrave and Richard Montgomery and Bhargav Narayanan",
year = "2022",
month = mar,
day = "31",
doi = "10.4171/JEMS/1101",
language = "English",
volume = "24",
pages = "303--339",
journal = "Journal of the European Mathematical Society",
issn = "1435-9855",
publisher = "European Mathematical Society Publishing House",
number = "1",

}

RIS

TY - JOUR

T1 - Spanning surfaces in 3-graphs

AU - Georgakopoulos, Agelos

AU - Haslegrave, John

AU - Montgomery, Richard

AU - Narayanan, Bhargav

PY - 2022/3/31

Y1 - 2022/3/31

N2 - 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 3n​ +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 3n​ +o(n) contains a spanning triangulation of the sphere.

AB - 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 3n​ +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 3n​ +o(n) contains a spanning triangulation of the sphere.

U2 - 10.4171/JEMS/1101

DO - 10.4171/JEMS/1101

M3 - Journal article

VL - 24

SP - 303

EP - 339

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

SN - 1435-9855

IS - 1

ER -