Georgia Institute of Technology College of Sciences

In the mid 1990s, Thomassen proved that planar graphs are 5-list-colourable, and that planar graphs of girth at least five are 3-list-colourable. Moreover, it can be shown via a simple degeneracy argument that planar graphs of girth at least four are 4-list-colourable.  In 2021, Postle and I unified these results, showing that if $G$ is a planar graph and $L$, a list assignment for $G$ where all vertices have size at least three; vertices in 4-cycles have list size at least four; and vertices in triangles have list size at least five, then $G$ is $L$-colourable. In this talk, I will discuss a strengthening of this latter result: that it also holds for correspondence colouring, a generalization of list colouring. In fact, it holds even in the still stronger setting of weak degeneracy. I will also speak briefly on some other weak degeneracy results in the area.

No prior knowledge of correspondence colouring nor list colouring will be assumed.  (Ft. joint work with Ewan Davies, and with Anton Bernshteyn and Eugene Lee.)