Abstract:
The problem of finding edge-disjoint trees in a hypercube arises for example in the context of parallel computing [3].
Independently of applications it is of high aesthetic appeal. The hypercube of dimension n, denoted by Qn, comprises 2n
vertices each corresponding to a distinct binary string of length n. Two vertices are adjacent if and only if their corresponding
binary strings differ in exactly one position. Since each vertex of Qn has degree n, the number of edges is n2n−1. A variety of
decomposability options derive from this fact. In the remainder of the introduction we focus on three of them. The first two
have been dealt with before in the literature; the third is the topic of this article.
