Stiebitz's degree partition conjecture.

The minimum outdegree of an oriented graph is denoted by δ⁺. In this problem, large could be replaced by some value. Like maybe 5?

If the indegree is bounded above, the partition exists. This is a direct application of Lovász' Local Lemma. If we just ask for δ⁺ at least 1 in the subgraphs, then minimum outdegree 3 suffices. This easily follows from a result of Carsten Thomassen asserting that δ⁺ at least 3 implies two vertex-disjoint circuits.