A seminal review of the b-chromatic number and related topics further consolidates these advances, emphasising important theoretical results and their potential computational challenges [3].

Dimitris Achlioptas, Assaf Naor, The Two Possible Values of the Chromatic Number of a Random Graph, Annals of Mathematics, Second Series, Vol. 162, No. 3 (Nov., 2005), pp. 1335-1351 ...

This paper proves that for any integer n ≥ 4 and any rational number r, 2 ≤ r ≤ n — 2, there exists a graph G which has circular chromatic number r and which does not contain Kn as a minor.