Janzer Olivér: The extremal number of subdivisions címmel

For a graph $H$, the extremal number (or Tur\'an number) $\mathrm{ex}(n,H)$ is defined to be the maximal number of edges in an $H$-free graph on $n$ vertices. For bipartite graphs $H$, determining the order of magnitude of $\mathrm{ex}(n,H)$ is notoriously difficult. In this talk I present recent progress on this problem.

The $k$-subdivision of a graph $F$ is obtained by replacing the edges of $F$ with internally vertex-disjoint paths of length $k+1$. Most of our results concern the Tur\'an number of various subdivided graphs, especially the subdivisions of the complete graph and the complete bipartite graph.

Partially joint work with David Conlon and Joonkyung Lee.