Weighted Regularity Lemma with Applications
B\'ela Csaba, Andr\'as Pluh\'ar

TL;DR
This paper extends the Regularity Lemma to weighted graphs, enabling applications to random graphs and weighted extremal graph theory, while managing exceptional sets effectively.
Contribution
It introduces a weighted version of the Regularity Lemma with techniques to control exceptional sets, broadening its applicability.
Findings
Extended Regularity Lemma applicable to weighted graphs
Applications to random graphs and weighted Erdős-Stone theorem
Methods to handle exceptional sets in weighted graph analysis
Abstract
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.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph theory and applications · Advanced Graph Theory Research
