Szemeredi''s Regularity Lemma and its applications in graph theory

摘要: Szemer\''edi''s Regularity Lemma is an important tool in discrete mathematics. It says that, some sense, all graphs can be approximated by random-looking graphs. Therefore the lemma helps proving theorems for arbitrary whenever corresponding result easy random Recently quite a few new results were obtained using Lemma, and also variants generalizations appeared. In this survey we describe typical applications generalizations.