Regularity lemmas in a Banach space setting
Abstract
Szemer\'edi's regularity lemma is a fundamental tool in extremal graph theory, theoretical computer science and combinatorial number theory. Lov\'asz and Szegedy [L. Lov\'asz and B. Szegedy: Szemer\'edi's Lemma for the analyst, Geometric and Functional Analysis 17 (2007), 252-270] gave a Hilbert space interpretation of the lemma and an interpretation in terms of compact- ness of the space of graph limits. In this paper we prove several compactness results in a Banach space setting, generalising results of Lov\'asz and Szegedy as well as a result of Borgs, Chayes, Cohn and Zhao [C. Borgs, J.T. Chayes, H. Cohn and Y. Zhao: An Lp theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions, arXiv preprint arXiv:1401.2906 (2014)].
Keywords
Cite
@article{arxiv.1502.04849,
title = {Regularity lemmas in a Banach space setting},
author = {Guus Regts},
journal= {arXiv preprint arXiv:1502.04849},
year = {2015}
}
Comments
15 pages. The topological part has been substantially improved based on referees comments. To appear in European Journal of Combinatorics