Abstract
For a positive integer d, the usual d-dimensional cube Qd is defined to be the graph (K2)d, the Cartesian product of d copies of K2. We define the generalized cube Q(Kk, d) to be the graph (Kk)d for positive integers d and k. We investigate the decomposition of the complete multipartite graph K into factors that are vertex-disjoint unions of generalized cubes Q(Kk, di), where k is a power of a prime, n and j are positive integers with j ≤ n, and the di may be different in different factors. We also use these results to partially settle a problem of Kotzig on Qd-factorizations of Kn. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 144–150, 2000
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