Subgraph entropy

Document Type

Journal Article

Role

Author

Published In

Bulletin of the London Mathematical Society

Volume

58

Issue

6

Article Number

e70397

Publication Date

6-1-2026

Abstract

Given �� ⩾ 3, we prove that there exists �� > 0 depending only on �� so that if �� is a metric graph of rank �� with met- ric entropy 1, then there exists a proper subgraph �� of �� with metric entropy at least ��. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space.

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