Layered subgraphs of the hypercube

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• Kada Williams (Cambridge)
• Thursday 14 November 2024, 14:30-15:30
• MR12.

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First, we discuss an abstract property of hypercube subgraphs, demonstrating that a certain labelling of its edges guarantees its embedding. Furthermore, we show that imposing an additional condition can ensure that a labelled graph embeds in a layer of the hypercube. For example, the hypercube of dimension two embeds in a hypercube, yet cannot embed in a layer. We prove that such a graph can be taken to have arbitrarily large girth, and even to be induced as a subgraph of a hypercube.

This talk is part of the Combinatorics Seminar series.

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