  In an earlier paper (J. Phys. A: Math. Gen. 26 (1993) 4689) we introduced the
notion of cycle percolation in the Bose gas and conjectured that it occurs if
and only if there is Bose-Einstein condensation. Here we give a complete proof
of this statement for the perfect and the imperfect (mean-field) Bose gas and
also show that in the condensate there is an infinite number of macroscopic
cycles.
