Hyperbolic families, and Counting Colourings

Combinatorics Seminar
Friday, November 10, 2023 - 3:15pm for 1 hour (actually 50 minutes)
Skiles 308
Evelyne Smith-Roberge – Georgia Tech – esmithroberge3@gatech.eduhttps://esmirob.math.gatech.edu/
Tom Kelly

Langhede and Thomassen conjectured in 2020 that there exists a positive constant c such that every planar graph G with 5-correspondence assignment (L,M) has at least 2^{c v(G)} distinct (L,M)-colourings. I will discuss a proof of this conjecture (which relies on the hyperbolicity of a certain family of graphs), a generalization of this result to some other embedded graphs (again, relying on a hyperbolicity theorem), and a few open problems in the area. Everything presented is joint work with Luke Postle.