Chen, Lih, and Wu conjectured that for r≥3, the only connected graphs with maximum degree at most r that are not equitably r-colorable are Kr,r (for odd r) and Kr+1. If true, this would be a strengthening of the Hajnal–Szemerédi Theorem and Brooks’ Theorem. We extend their conjecture to disconnected graphs. For r≥6 the conjecture says the following: If an r-colorable graph G with maximum degree...
