A Mengerian theorem for paths of length at least three

Let be x, y two vertices of a graph G, such that t openly disjoint xy-paths of length ≥3 exist. In this article we show that then there exists a set S of cardinality less than or equal to 3t – 2, resp. 2t for t ∈ {1, 2, 3}, which destroys all xy-paths of length ≥3. Also a lower bound for the cardinality of S is given by constructing special graphs.