The separation profile of any δ-hyperbolic planar or apex-minor-free graph grows at most as C log n, answering Benjamini–Schramm–Timár affirmatively.
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Separation profiles of hyperbolic planar and apex-minor-free graphs
The separation profile of any δ-hyperbolic planar or apex-minor-free graph grows at most as C log n, answering Benjamini–Schramm–Timár affirmatively.