How does the complexity of calculating the Permanent imply the NP completeness of directed 3-cycle cover?

In their paper Two Approximation Algorithms for 3-Cycle Covers of Markus Bläser and Bodo Manthey it is stated that: "...deciding whether an unweighted directed graph has a 3-cycle cover is already NP-complete. This follows from the work of Valiant [16] (see also Garey and Johnson [7, GT 13])."

However I can't see what of Valiant's paper The Complexity of Computing the Permanent, resp. the simplified version by Ben-Dor and Halevi, should imply the stated NP-completeness; also GT13 Minimum Bottleneck Path Matching of Garey and Johnson seems to have no obvious relation to the stated complexity.

Questions:

• why does the NP-Completeness of deciding the existence of a directed vertex-disjoint cycle cover follow from Valiant's complexity result of calculating the Permanent?
• what is the transformation that demonstrates the equivalence of the Minimum Bottleneck Path Matching and deciding the existence of a directed vertex disjoint 3-cycle cover?

I have already done extensive googling, but could not find anything that could be cited as a proof of the claimed complexity of deciding the existence of a directed vertex-disjoint 3-cycle cover.

When I look in Garey and Johnson I find that [GT 13] is PARTITION INTO HAMILTONIAN SUBGRAPHS which is the problem of deciding if a $$3$$-cycle cover exists in a digraph. So, this could be used as a reference for the complexity. Also, Garey and Johnson cited the Valiant paper for this NP-complete problem.