Relaxed approximate coloring in exact maximum clique search. This paper presents selective coloring as a new paradigm for branch-and-bound exact maximum clique search. Approximate coloring has, in recent, years been at the heart of leading solvers in the field. Selective coloring proposes to relax coloring up to a certain threshold. The result is a less informed but lighter decision heuristic.par Different operators for the remaining uncolored vertices give rise to algorithmic variants integrated in a new BBMCL framework. BBMCL allows for an interesting comparison between approximate coloring and degree-based decision heuristics.par The paper also reports extensive empirical tests. Selective coloring algorithms are fastest for a large subset of the graphs considered.