Consider a graph C*-algebra C*(E) with a purely infinite ideal I (possibly
all of C*(E)) such that I has only finitely many ideals and C*(E)/I is
approximately finite dimensional. We prove that the nuclear dimension of C*(E)
is 1. If I has infinitely many ideals, then the nuclear dimension of C*(E) is
either 1 or 2.Comment: 24 pages; this version to appear in Adv. Mat
