Partitioning Two-Coloured Complete Graphs into Two Monochromatic Cycles
Combinatorics, Probability and Computing
The 3-colour ramsey number of a 3-uniform berge cycle
Combinatorics, Probability and Computing
Review: Measuring instance difficulty for combinatorial optimization problems
Computers and Operations Research
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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.