### Fractional chromatic number of graphs of bounded maximum degree

- Series
- Graph Theory Seminar
- Time
- Tuesday, February 16, 2021 - 15:45 for 1 hour (actually 50 minutes)
- Location
- https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
- Speaker
- Zdeněk Dvořák – Charles University – rakdver@iuuk.mff.cuni.cz

By the well-known theorem of Brooks, every graph of maximum degree Δ ≥ 3 and clique number at most Δ has chromatic number at most Delta. It is natural to ask (and is the subject of a conjecture of Borodin and Kostochka) whether this bound can be improved for graphs of clique number at most Δ - 1. While there has been little progress on this conjecture, there is a number of interesting results on the analogous question for the fractional chromatic number. We will report on some of them, including a result by myself Bernard Lidický and Luke Postle that except for a finite number of counterexamples, every connected subcubic triangle-free graph has fractional chromatic number at most 11/4.