Long path and cycle decompositions of even hypercubes
Maria Axenovich, David Offner, Casey Tompkins · European Journal of Combinatorics · 2021
We consider edge decompositions of the n-dimensional hypercube Qn into isomorphic copies of a given graph H. While a number of results are known about decomposing Qn into graphs from various classes, the simplest cases of paths and cycles of a given length are far from being understood. A conjecture of Erde asserts that if n is even, ℓ<2n and ℓ divides the number of edges of Qn, then the path of length ℓ decomposes Qn. Tapadia et al. proved that any path of length 2mn, where 2m