Séance Séminaire

Séminaire Gaston Darboux

Structure of quasi-transitive graphs : planarity, minor exclusion and more

A graph is quasi-transitive if the action of its automorphism group on its vertex set has finitely many orbits. Quasi-transitive graphs generalize in par- ticular Cayley graphs and vertex/edge-transitive graphs. In this presentation, I will give an overview of different recent structural results on quasi-transitive graphs. In the case of planar quasi-transitive graphs, I will present a generalization of a theorem of Droms (2006) allowing to decompose such a graph into simpler pieces. I will also present a structure theorem for quasi-transitive graphs which more generally exclude a finite or infinite graph as a minor, and I will discuss some applications. If the time permits, I will also mention a number of recent related questions and results on more general classes of quasi-transitive graphs that recently attired a lot of attention in Coarse graph theory. This talk is based on some joint works with Louis Esperet and Clément Legrand-Duchesne.