Irene Heinrich (TU Darmstadt) – Classifying coloured ultrahomogeneous graphs

I will give a talk on several recent results regarding ultrahomogeneous graphs. A relational structure R is ultrahomogeneous if every isomorphism of finite induced substructures of R extends to an automorphism of R. We classify the finite vertex-colored oriented ultrahomogeneous graphs and the finite vertex-colored undirected graphs. The classifications comprise new general methods which govern how graphs can be combined or extended to create new ultrahomogeneous graphs. Further, we extend a classic theorem of Cameron (every 5-tuple regular graph is already ultrahomogeneous) to the setting of colored graphs.

This is joint work with Sofia Brenner, Eda Kaja, Thomas Schneider, and Pascal Schweitzer.