Abstract
We prove that if m≥ 2, then the minimumk∈N such that the k -cube {0, 1}kcan be decomposed as the disjoint union of m connected adjacent subsets satisfies 2log2m−log2log2m− 1 ≤k≤ 2⌈log2m⌉ − ⌊log2log2m⌋ + 5.
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