Weighted Regularity Lemma with Applications

Béla Csaba, András Pluhár

Published 2009-07-01, updated 2011-02-12Version 2

We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means to handle the otherwise uncontrolled exceptional set.