Layered subgraphs of the hypercube
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913333363343360 |
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| author | Behague, Natalie Leader, Imre Morrison, Natasha Williams, Kada |
| author_facet | Behague, Natalie Leader, Imre Morrison, Natasha Williams, Kada |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Layered subgraphs of the hypercube Behague, Natalie Leader, Imre Morrison, Natasha Williams, Kada Combinatorics 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. |
| title | Layered subgraphs of the hypercube |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.18014 |