The open problems session is next week! There are two sessions: Session 1 loosely focused on matroids and Session 2 loosely focused on graphs. Anyone interested in the topics is welcome to join; no registration is required. The sessions will not be recorded, but we will update this page linking to the slide(s) of each presenter.

**Date:**Monday, December 14 (1:30 – 4:00pm ET)

**Schedule:**

Session 1 (matroids)

**:**1:30 – 2:30pm ETSession 2 (graphs)

**:**3:00 – 4:00pm ETBeer time

**:**After that 🙂**Format:**We’ll have a short presentation about each problem followed by some time for discussion. There will likely be time at the end for further impromptu problems as well. We will also link to a Discord server as a suggested way of discussing problems via text.

**Session 1 presenters:**

Nathan Bowler – slides

Daniel Bernstein – slides

Dillon Mayhew – slides

Peter Nelson – slides

Relinde Jurrius – slides

Jim Geelen – slides

**Session 2 presenters:**

Maria Chudnovsky – slides

Youngho Yoo – slides

Chun-Hung Liu – slides

Ben Moore – slides

Johannes Carmesin – slides

Rose McCarty – slides

Ben Moore pointed out that my wild conjecture is false. Take G to be a graph with very small fraction chromatic number but large chromatic number and take H to be a graph with fraction chromatic number larger than that of G, and with huge girth (such graphs exist).

Maybe the conjecture can be rectified by changing “chromatic number” to “fractional chromatic number”.

Nathan’s question about my conjecture is an interesting one: are there only countably many classes of graphs that are closed and well-quasi-ordered under the induced subgraph relation. I believe a negative answer to this question will imply a negative answer to my conjecture.