The Blow-up Lemma

Authors:
János Komlós
Affiliations:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: komlos@math.rutgers.edu)
Venue:
Combinatorics, Probability and Computing
Year:
1999

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Abstract

Extremal graph theory has a great number of conjectures concerning the embedding of large sparse graphs into dense graphs. Szemerédi's Regularity Lemma is a valuable tool in finding embeddings of small graphs. The Blow-up Lemma, proved recently by Komlós, Sárközy and Szemerédi, can be applied to obtain approximate versions of many of the embedding conjectures. In this paper we review recent developments in the area.