Minimum cutsets in hypercubes

A local cut at a vertex v is a set consisting of, for each neighbor x of v, the vertex x or the edge vx. We prove that the local cuts are the smallest sets of vertices and/or edges whose deletion disconnects the k-dimensional hypercube Q"k. We also characterize the smallest sets of vertices and/or edges whose deletion produces a graph with larger diameter than Q"k. These are the sets consisting of k-1 elements from a local cut.