Caleb Fong, Rutgers University

Abstract

The Unfriendly Partition Conjecture posits that every countable graph can be bipartitioned in such a way that each vertex has more neighbours outside its own part (i.e., has an unfriendly partition). This is still wide open, so I will also talk about some variations of this study in the context of directed graphs and list colouring. We will hopefully encounter different flavours of proof (compactness, probabilistic, linear algebraic) and several open problems.

See: https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html