Decomposing the hypercube Qn into n isomorphic edge-disjoint trees

Wagner, Stephan
Wild, Marcel
Journal Title
Journal ISSN
Volume Title
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.
The original publication is available at
The pre-print of this article can be found at
Hypercubes, Decomposition, Isomorphic trees, Edge-disjoint trees
Wagner, S. & Wild, M. 2012. Decomposing the hypercube Qn into n isomorphic edge-disjoint trees. Discrete Mathematics, 312(10), 1819-1822, doi:10.1016/j.disc.2012.01.033.