English

Layered subgraphs of the hypercube

Combinatorics 2024-04-30 v1

Abstract

A subgraph of the nn-dimensional hypercube is called 'layered' if it is a subgraph of a layer of some hypercube. In this paper we show that there exist subgraphs of the cube of arbitrarily large girth that are not layered. This answers a question of Axenovich, Martin and Winter. Perhaps surprisingly, these subgraphs may even be taken to be induced.

Keywords

Cite

@article{arxiv.2404.18014,
  title  = {Layered subgraphs of the hypercube},
  author = {Natalie Behague and Imre Leader and Natasha Morrison and Kada Williams},
  journal= {arXiv preprint arXiv:2404.18014},
  year   = {2024}
}

Comments

11 pages

R2 v1 2026-06-28T16:08:40.874Z