Martin Balko: Ordered graphs and Ramsey numbers

We introduce ordered Ramsey numbers, which are an analogue of Ramsey numbers for ordered graphs. That is, for graphs with a linear order on their vertex sets. We survey recent results about ordered Ramsey numbers with emphasis on bounded-degree ordered graphs. We show that ordered Ramsey numbers can behave very differently when compared with the standard Ramsey nubmers. We also mention several open problems in this area. Some parts of this talk are based on joint works with Josef Cibulka, Jan Kynčl, and Karel Král and with Vít Jelínek and Pavel Valtr.