The Blow-up Lemma

1999 ◽  
Vol 8 (1-2) ◽  
pp. 161-176 ◽  
Author(s):  
JÁNOS KOMLÓS
Keyword(s):  
Graph Theory ◽  
Blow Up ◽  
Extremal Graph ◽  
Extremal Graph Theory ◽  
Regularity Lemma ◽  
Sparse Graphs ◽  
Dense Graphs ◽  
Recent Developments ◽  
Szemeredi's Regularity Lemma

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.

scholarly journals Szemerédi's Regularity Lemma for Matrices and Sparse Graphs

2011 ◽  
Vol 20 (3) ◽  
pp. 455-466 ◽  
Author(s):  
ALEXANDER SCOTT
Keyword(s):  
Local Density ◽  
Regularity Lemma ◽  
Density Condition ◽  
Sparse Graphs ◽  
Dense Graphs ◽  
Szemeredi's Regularity Lemma ◽  
Real Matrices

Szemerédi's Regularity Lemma is an important tool for analysing the structure of dense graphs. There are versions of the Regularity Lemma for sparse graphs, but these only apply when the graph satisfies some local density condition. In this paper, we prove a sparse Regularity Lemma that holds for all graphs. More generally, we give a Regularity Lemma that holds for arbitrary real matrices.

scholarly journals Extremal graph theory and finite forcibility

2017 ◽  
Vol 61 ◽  
pp. 541-547
Author(s):  
Andrzej Grzesik ◽  
Daniel Král' ◽  
László Miklós Lovász
Keyword(s):  
Graph Theory ◽  
Extremal Graph ◽  
Extremal Graph Theory

Extremal Graph Theory

2020 ◽  
pp. 33-56
Author(s):  
Fan Chung ◽  
Ron Graham
Keyword(s):  
Graph Theory ◽  
Extremal Graph ◽  
Extremal Graph Theory
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