  Beck's conjecture on coloring of graphs associated to various algebraic
objects has generated considerable interest in the community of discrete
mathematics and combinatorics since its inception in the year 1988. The version
of this conjecture for power-graphs of finite groups has been addressed and
partially settled by previous authors. In this paper we answer it in the
affirmative in complete generality, and, in effect, we establish a "nicer"
statement on a larger class of graphs. We also clear up certain ambiguities
present in the way the previous versions of the conjecture were posed.
