Let D be a connected, locally semicompletedigraph with p ≥ 4 strong components and acyclic ordering D1, D2, ..., Dp of these. Suppose that V (D1) = {u1} and V (Dp) = {v1} and that D − x is connected for every vertex x. Then for every choice of u2 ∈ V (D2) and v2 ∈ V (Dp−1), D has two vertex disjoint paths P1 from u2 to v1 and P2 from u1 to v2 with V (P1) ∪ V (P2) = V (D) if and only if D is not an odd chain from u1 to v1.

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