Ruszinkó Miklós (Rényi Intézet): Monochromatic connected matchings

The proof technique of monochromatic connected matchings has been initiated by Łuczak. This method is based on the Szemerédi Lemma and it is a useful tool in proving Ramsey type results. Proofs of some theorems using this technique will be sketched altogether with some seemingly easy open problems in Ramsey theory.