On \(k\)-partitioning of Hamming graphs (Q1302152)

For a graph \(G=(V,E)\) a \(k\)-partition is a partition \(A=\{A_1, A_2, \dots, A_k \}\) of \(V\) such that \(||A_i|- |A_j||\leq 1\) for all \(i,j\in \{1,2,\dots, k\}\). A cut of partition \(A\) is a set of edges having ends in different sets of the partition. The authors investigate the problem of determining \(k\)-partitions with minimal cardinality cut. Several interesting bounds and asymptotic results for some specific values of \(k\) are presented for Hamming graphs (Cartesian products of complete graphs).