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 nux. 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. (C) 2004 Elsevier B.V. All rights reserved.