**Monday, March 15,** **3pm ET** (7pm GMT, 8am Tue NZDT)**Benjamin Moore**, University of Waterloo**A density bound for triangle free 4-critical graphs**

**Zoom: **https://us02web.zoom.us/j/89998025625**Password**: email rose.mccarty ~at~ uwaterloo ~.~ ca if you need the password

**Abstract:**

Carsten Thomassen showed that every girth 5 graph embeddable in the torus or projective plane is 3-colourable. A complementary result of Robin Thomas and Barrett Walls shows that every girth 5 graph embedded in the Klein bottle is 3-colourable.

I’ll show neither the embeddability condition nor the girth 5 condition is needed in the above theorems by showing that every triangle-free 4-critical graph has average degree slightly larger than 10/3.

This is joint work with Evelyne Smith Roberge.