On k-partitioning of Hamming graphs Original Research Article

We consider the graphs Han defined as the Cartesian products of n complete graphs with a vertices each. Let an edge cut partition the vertex set of a graph into k subsets A1,…,Ak with ||Ai|−|Aj||⩽1. We consider the problem of determining the minimal size of such a cut for the graphs defined above and present bounds and asymptotic results for some specific values of k.