Geodesic
Layered subgraphs of the hypercube
Natalie Behague1 ; Imre Leader2 ; Natasha Morrison ; Kada Williams2
1University of Warwick
2University of Cambridge
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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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.
DOI : 10.37236/12980
Classification : 05D05, 05C35, 05C65
Mots-clés : positive Turán density, cubical graph

Natalie Behague  1   ; Imre Leader  2   ; Natasha Morrison    ; Kada Williams  2

1 University of Warwick
2 University of Cambridge 
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     title = {Layered subgraphs of the hypercube},
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     year = {2024},
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     doi = {10.37236/12980},
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Natalie Behague; Imre Leader; Natasha Morrison; Kada Williams. Layered subgraphs of the hypercube. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12980

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