The generalized 4-connectivity of hypercubes

The connectivity and the spanning tree packing number of a graph are two important measurements for the fault-tolerance of a network. The generalized connectivity is a common generalization of the classical connectivity and spanning tree packing number. In this paper, we show that the generalized 4-connectivity of the n-dimensional hypercube Qn is (n−1), that is, for any four vertices in Qn, there exist (n−1) internally disjoint trees connecting them in Qn.