Despite it being a seemingly redundant topic, the task of colouring bipartite graphs has a surprisingly rich tradition, connecting to different parts of combinatorics. I am referring here of course to stronger forms of graph colouring, especially those related to list colouring. I will give a quick overview of some highlights in this vein starting with the seminal Erdős-Rubin-Taylor paper, and spanning links to, inter alia, Property B, hypergraph Turán numbers, the coupon collector problem, the local lemma, and the permanent in random matrices. Central to these investigations is the stubborn Alon-Krivelevich conjecture, and a view towards chromatic structure in triangle-free graphs.
This talk touches on recent joint works with, variously, Alon, Cambie, Cames van Batenburg, and Davies.