In the mathematics of directed graphs, the Lucchesi–Younger theorem is a relationship between dicuts and dijoins.
It was published by Cláudio L. Lucchesi and Daniel H. Younger in 1978.
[1][2] Their proof resolved a conjecture that had been posed roughly a decade earlier by Younger,[3] and in unpublished work by Neil Robertson,[2] motivated by the duality in planar graphs between dijoins and feedback arc sets.
Therefore, the maximum number of disjoint dicuts in any graph must be less than or equal to the minimum size of a dijoin.
The minimum size of a dijoin equals the maximum number of disjoint dicuts that can be found in a given graph.