Where can I find a proof of Thompson's Theorem regarding existence of disjoint cycles in graph with outward degree at least 3?

Question

I am looking for a proof of thompson's theorem: Given a directed graph with outward degree at least 3 for each vertex, there exist 2 vertex disjoint directed cycles. I can only find it behind a paywall here https://link.springer.com/article/10.1007/BF02579195 .

But it's from freaking 1984 so I hope there is a free proof.

Thanks

Answer 1

This article does $k=3$ in the Bermond-Thomassen conjecture, but also gives a stronger version of the 1983 result, $k=2, $ which gives you what you want.

There does not seem to be anyone involved named Thompson.

See http://www.openproblemgarden.org/op/the_bermond_thomassen_conjecture