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 𝑟 ⩾3, we prove that there exists 𝜆 >0 depending only on 𝑟 so that if 𝐺 is a metric graph of rank 𝑟 with metric entropy 1, then there exists a proper subgraph 𝐻 of 𝐺 with metric entropy at least 𝜆. 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.
Suggested Citation
Hamed, T., Aougab, Tarik (Mathematics & Statistics), & Clay, M. (2026). Subgraph entropy. Bulletin of the London Mathematical Society, 58(6), e70397. https://doi.org/10.1112/blms.70397
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