- Series
- Graph Theory Seminar
- Time
- Tuesday, September 6, 2022 - 3:45pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Evelyne Smith-Roberge – Georgia Tech – esmithroberge3@gatech.edu – http://www.math.uwaterloo.ca/~e2smithr/
- Organizer
- Tom Kelly
Thomassen famously showed that every planar graph is 5-choosable, and that every planar graph of girth at least five is 3-choosable. These theorems are best possible for uniform list assignments: Voigt gave a construction of a planar graph that is not 4-choosable, and of a planar graph of girth four that is not 3-choosable. In this talk, I will introduce the concept of a local girth list assignment: a list assignment wherein the list size of each vertex depends not on the girth of the graph, but only on the length of the shortest cycle in which the vertex is contained. I will present a local list colouring theorem that unifies the two theorems of Thomassen mentioned above and discuss some of the highlights and difficulties of the proof. This is joint work with Luke Postle.