Pat Morin, Carleton University

In this talk, I will review progress on adjacency labelling and induced-universal graphs for various minor-closed and non-minor-closed families of graphs. I will then show that every proper minor-closed class of graphs has a (1 + o(1))log n-bit adjacency labelling scheme. Equivalently, for every proper minor-closed graph family ℱ and every positive integer n, there exists an n^1+o(1)-vertex graph U_n such that every n-vertex graph G in ℱ is isomorphic to some induced subgraph of U_n.

This is joint work with Vida Dujmović, Louis Esperet, Cyril Gavoille, Gwenaël Joret, Piotr Micek, and David R. Wood.