Separation and treewidth profiles of graphs are asymptotically equivalent, with explicit calculations for Cayley graphs of tree-graded graphs including those of free products of finitely generated groups.
Poincar\'e profiles of lamplighter diagonal products
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Separation profiles of free products
Separation and treewidth profiles of graphs are asymptotically equivalent, with explicit calculations for Cayley graphs of tree-graded graphs including those of free products of finitely generated groups.