Layered subgraphs of the hypercube
Combinatorics
2024-04-30 v1
Abstract
A subgraph of the -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.
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