Directed vertex-connectivity augmentation

The problem of finding a smallest set of new edges to be added to a given d irected graph to make it k-vertex-connected was shown to be polynomially so lvable recently in [6] for any target connectivity k greater than or equal to 1. However, the algorithm given there relied on the ellipsoid method. He re we refine some results of [6] which makes it possible to construct a com binatorial algorithm which is polynomial for any Bred k. Short proofs for ( extensions of) some earlier results related to this problem will also be gi ven.