1Department of Mathematics and Computer Science, Ariel University, Israel 2University of Oxford 3Universidad de Santiago de Chile 4Technische Universität Ilmenau 5Universität Hamburg
The electronic journal of combinatorics, Tome 25 (2018) no. 3
An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical' properties are asymptotically equivalent and, thus, a graph $G$ possessing one such property automatically satisfies the others.In recent years, work in this area has focused on uncovering more quasirandom graph properties and on extending the known results to other discrete structures. In the context of hypergraphs, however, one may consider several different notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. We give short and purely combinatorial proofs of the main equivalences in Towsner's result.
Elad Aigner-Horev
1
;
David Conlon
2
;
Hiệp Hàn
3
;
Yury Person
4
;
Mathias Schacht
5
1
Department of Mathematics and Computer Science, Ariel University, Israel
2
University of Oxford
3
Universidad de Santiago de Chile
4
Technische Universität Ilmenau
5
Universität Hamburg
@article{10_37236_7537,
author = {Elad Aigner-Horev and David Conlon and Hiệp H\`an and Yury Person and Mathias Schacht},
title = {Quasirandomness in hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/7537},
zbl = {1395.05182},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7537/}
}
TY - JOUR
AU - Elad Aigner-Horev
AU - David Conlon
AU - Hiệp Hàn
AU - Yury Person
AU - Mathias Schacht
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JO - The electronic journal of combinatorics
PY - 2018
VL - 25
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Elad Aigner-Horev; David Conlon; Hiệp Hàn; Yury Person; Mathias Schacht. Quasirandomness in hypergraphs. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7537
