Cyclic type factorizations of complete bipartite graphs into hypercubes

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Abstract

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 languageEnglish (US)
Pages (from-to)201-209
Number of pages9
JournalAustralasian Journal of Combinatorics
Volume25
StatePublished - Dec 1 2002

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