Let G = (V,E) be a k-connected graph, T a k-subset of V , and s ∈ V T. Show that there exists a set of
k paths with start vertex s and end vertex in T for which no two of these paths share a vertex other than s. Show that Theorem 8.1.4 is best possible by constructing (for each choice of κ(G)) a graph G with α(G) = κ(G) + 1 which is not Hamiltonian.