Table of Contents
International Journal of Combinatorics
Volume 2014 (2014), Article ID 602657, 9 pages
http://dx.doi.org/10.1155/2014/602657
Research Article

A Weighted Regularity Lemma with Applications

1Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged 6724, Hungary
2Department of Computer Science, University of Szeged, Árpád tér 2, Szeged 6720, Hungary

Received 13 February 2014; Revised 27 May 2014; Accepted 27 May 2014; Published 19 June 2014

Academic Editor: Laszlo A. Szekely

Copyright © 2014 Béla Csaba and András Pluhár. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove an extension of the regularity lemma with vertex and edge weights which in principle can be applied for arbitrary graphs. The applications involve random graphs and a weighted version of the Erdős-Stone theorem. We also provide means to handle the otherwise uncontrolled exceptional set.