## Szemerédi's Regularity Lemma and Its Applications in Graph Theory (1996)

Citations: | 202 - 3 self |

### BibTeX

@MISC{Komlós96szemerédi'sregularity,

author = {János Komlós and Miklós Simonovits},

title = {Szemerédi's Regularity Lemma and Its Applications in Graph Theory},

year = {1996}

}

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### Abstract

Szemer'edi's Regularity Lemma is an important tool in discrete mathematics. It says that, in some sense, all graphs can be approximated by random-looking graphs. Therefore the lemma helps in proving theorems for arbitrary graphs whenever the corresponding result is easy for random graphs. Recently quite a few new results were obtained by using the Regularity Lemma, and also some new variants and generalizations appeared. In this survey we describe some typical applications and some generalizations. Contents Preface 1. Introduction 2. How to apply the Regularity Lemma 3. Early applications 4. Building large subgraphs 5. Embedding trees 6. Bounded degree spanning subgraphs 7. Weakening the Regularity Lemma 8. Strengthening the Regularity Lemma 9. Algorithmic questions 10. Regularity and randomness Preface Szemer'edi's Regularity Lemma [121] is one of the most powerful tools of (extremal) graph theory. It was invented as an auxiliary lemma in the proof of the famous conjectu...