Decompositions of even hypercubes into cycles whose length is a power of two

TL;DR

This paper demonstrates that even-dimensional hypercubes can be decomposed into edge-disjoint cycles of lengths that are powers of two, covering all such cycle lengths from 4 up to 2^n.

Contribution

It provides a comprehensive decomposition of even hypercubes into cycles of specific power-of-two lengths, extending previous understanding of hypercube cycle structures.

Findings

Hypercubes can be decomposed into cycles of length 2^i for all i from 2 to n.

The decomposition covers all such cycle lengths within the specified range.

This advances the understanding of hypercube cycle decompositions.

Abstract

If $n$ is even, the $n$-dimensional hypercube can be decomposed into edge-disjoint cycles of length $2^i$ for every value of $i$ from $2$ to $n$.