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arXiv · 2604.24462

Separation profiles of free products

David Hume
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Abstract

We deduce from a theorem of Dvorak--Norin that the separation and treewidth profiles of graphs are asymptotically equivalent, resolving a question of Huang--Hume--Kelly--Lam. As an application, we calculate the separation profiles of Cayley graphs of tree-graded graphs in terms of their pieces. Examples of tree-graded graphs include Cayley graphs of free products of finitely generated groups.

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David Hume. 2026-04-27. Separation profiles of free products. https://arxiv.org/abs/2604.24462

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