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arXiv · 2404.18014

Layered subgraphs of the hypercube

Natalie Behague·Imre Leader·Natasha Morrison·Kada Williams
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Abstract

A subgraph of the $n$-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.

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Natalie Behague, Imre Leader, Natasha Morrison, Kada Williams. 2024-04-27. Layered subgraphs of the hypercube. https://arxiv.org/abs/2404.18014

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