So far, the smallest complete bipartite graph which was known to have a cyclic type decomposition into cubes Qd of a given dimension d was Kd2d-2,d2d-2. Using binary Hamming codes we prove in this paper that there exists a cyclic type factorization of K2d-1,2d-1 into Qd if and only if d is a power of 2.
|Original language||English (US)|
|Number of pages||9|
|Journal||Australasian Journal of Combinatorics|
|State||Published - Dec 1 2002|