TL;DR
This paper establishes the asymptotic equivalence of separation and treewidth profiles in graphs, and applies this to compute separation profiles of Cayley graphs of free products of groups.
Contribution
It proves the asymptotic equivalence of separation and treewidth profiles, resolving a question in graph theory, and computes these profiles for Cayley graphs of free products.
Findings
Separation and treewidth profiles are asymptotically equivalent.
Separation profiles of Cayley graphs of free products are explicitly calculated.
Addresses a question posed by Huang--Hume--Kelly--Lam.
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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