A Simple Regularization of Hypergraphs
Combinatorics
2009-04-30 v2 Number Theory
Abstract
We give a simple and natural (probabilistic) construction of hypergraph regularization. It is done just by taking a constant-bounded number of random vertex samplings only one time (thus, iteration-free). It is independent from the definition of quasi-randomness and yields a new elementary proof of a strong hypergraph regularity lemma. Consequently, as an example of its applications, we have a new self-contained proof of Szemer\'edi's classic theorem on arithmetic progressions (1975) as well as its multidimensional extension by Furstenberg-Katznelson (1978).
Cite
@article{arxiv.math/0612838,
title = {A Simple Regularization of Hypergraphs},
author = {Yoshiyasu Ishigami},
journal= {arXiv preprint arXiv:math/0612838},
year = {2009}
}
Comments
16 pages