English

A Highly Symmetric Hamilton Decomposition for Hypercubes

Combinatorics 2020-04-07 v1

Abstract

A Hamilton decomposition of a graph is a partitioning of its edge set into disjoint spanning cycles. The existence of such decompositions is known for all hypercubes of even dimension 2n2n. We give a decomposition for the case n=2a3bn = 2^a3^b that is highly symmetric in the sense that every cycle can be derived from every other cycle just by permuting the axes. We conjecture that a similar decomposition exists for every n.

Keywords

Cite

@article{arxiv.2004.02750,
  title  = {A Highly Symmetric Hamilton Decomposition for Hypercubes},
  author = {Farid Bouya and Ebadollah S. Mahmoodian and Modjtaba Shokrian Zini and Mojtaba Tefagh},
  journal= {arXiv preprint arXiv:2004.02750},
  year   = {2020}
}
R2 v1 2026-06-23T14:41:16.629Z