Dicut

[2] In planar graphs, dicuts and cycles are dual concepts.

For a dicut in the given graph, the duals of the edges that cross the dicut form a directed cycle in the dual graph, and vice versa.

Woodall's conjecture, an unsolved problem in this area, states that in any directed graph the minimum number of edges in a dicut (the unweighted minimum closure) equals the maximum number of disjoint dijoins that can be found in the graph (a packing of dijoins).

[1][4] A fractional weighted version of the conjecture, posed by Jack Edmonds and Rick Giles, was refuted by Alexander Schrijver.

[5][6][1] In the other direction, the Lucchesi–Younger theorem states that the minimum size of a dijoin equals the maximum number of disjoint dicuts that can be found in a given graph.

All edges crossing between the subsets go from Subset 1 to Subset 2, so a partition of the set into these subsets is a dicut. Subset 2 is a closure because there are no edges which exit it.