Limits of Hypergraphs, Removal and Regularity Lemmas. A Non-standard Approach

By Gábor Elek, Balázs Szegedy. 2007

70 citations recorded by the source corpus.

We study the integral and measure theory of the ultraproduct of finite sets. As a main application we construct limit objects for hypergraph sequences. We give a new proof for the Hypergraph Removal Lemma and the Hypergraph Regularity Lemma.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1a84bc591344e68826fdd4c982bb00ea5ff533ac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Tim Austin

In Discrete Mathematics and Combinatorics

1. Tim Austin
2. Nikos Frantzikinakis
3. Sourav Chatterjee
4. Xiangdong Ye
5. S. Shao
6. Dmitry Panchenko

In Geometry and Topology

1. Tim Austin
2. Nikos Frantzikinakis
3. Sourav Chatterjee
4. S. Shao
5. Xiangdong Ye

Citations in the corpus

• On exchangeable random variables and the statistics of large graphs and hypergraphs (2008, methodology): “In fact, Elek and Szegedy’s use of ultralimits has a predecessor in Hoover’s approach to the basic representation theorems for exchangeable arrays of random variables, as outlined in [42].”