Minimum cutsets in hypercubes

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