This week's seminar is given by Andrzej Grzesik from Jagiellonian University, Poland.
Title: Rainbow Turán problems
Abstract: A typical Turán problem asks for the maximum number of edges in graphs that do not contain a given forbidden graph. In the rainbow variant of this problem, we consider many graphs on a common vertex set, thinking of each graph as edges in a separate color, and want to determine the smallest number of edges in each color that guarantees the existence of a rainbow copy of a given graph. In the talk we will survey known results on this topic, in particular present the asymptotically optimal solution for short paths, directed triangles and small directed stars for any number of colors. This is based on joint works with Sebastian Babiński, Dániel Gerbner, Cory Palmer and Magdalena Prorok.
