We continue the investigation of Borel and Lebesgue measurable graph colorings. This time we focus on "negative" results, i.e., situations in which these definable chromatic numbers differ substantially from the classical chromatic numbers. Additionally, we examine the possibility of a G0-like dichotomy occurring between graphs of finite Borel chromatic number and those of infinite Borel chromatic number.
This is joint work with Alexander S. Kechris and Benjamin D. Miller.