A Note on the Vertex-Connectivity Augmentation Problem

Using the polynomial algorithm given in [T. Jordán, On the optimal vertex-connectivity augmentation,J. Combin. Theory Ser. B63(1995), 8–20] ak-connected undirected graphG=(V, E) can be made (k+1)-connected by adding at mostk−2 surplus edges over (a lower bound of) the optimum. Here we introduce two new lower bounds and show that in fact the size of the solution given by (a slightly modified version of) this algorithm differs from the optimum by at most ⌈(k−1)/2⌉.