Paths partition with prescribed beginnings in digraphs: A Chvátal-Erdős condition approach (Q941336)

A digraph is said to verify the Chvatal-Erdős conditions if its stability number is not larger than its vertex connectivity. It is shown that for every set of 2 vertices x and y, there exists a vertex-partition of the digraph into directed paths P1 and P2 such that P1 begins at x and P2 begins at y. It is conjectured that this is true for any number of vertices of the digraph in the set.