Mini-course by Gábor Tardos "Extremal theory of vertex- and edge-ordered graphs"
Gábor Tardos gave 3 lectures diving into extremal theory of vertex- and edge-ordered graphs in details. The talks took place in the Moscow Institute of Physics and Technology in November 2019, with extended . Two of them were the part of the "Combinatorics and Geometry Days I" conference. And also there was the separate final lecture the day after the conference.
Here are the recordings of all three lectures:
"The basic question of Turan type extremal graph theory is the maximum number of edges in a simple graph on n vertices that does not contain a specified "forbidden" subgraph (or any one of several forbidden subgraphs). This is a classical topic of combinatorics with many deep results and lot of questions that are still open.
In my survey talk I will focus on extensions of this theory to simple graphs with an additional structure, namely a linear order on the set of vertices or edges. A single simple graph has several vertex order and by forbidding just one of them we obtain different extremal questions. Introducing either a vertex- or an edge-order makes the theory richer and more suitable to (mostly geometric) applications.
I will highlight several specific open problems about both vertex- and edge-ordered graphs. I will mention results from numerous researchers, among them Balazs Keszegh, Daniel Korandi, Jesse Geneson, Daniel Gerbner, Adam Marcus, Abhishek Methuku, Daniel Nagy, Janos Pach, Seth Pettie, Domotor Palvolgyi, Istvan Tomon, Mate Vizer, Creig Weidert, etc."
Find more talks by Gábor Tardos on this page.