Subgraph Entropy

Tarik Aougab; Matt Clay; Tawfiq Hamed

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arXiv · 2506.18838

Subgraph Entropy

Tarik Aougab·Matt Clay·Tawfiq Hamed

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Abstract

Given $r \geq 3$, we prove that there exists $\lambda >0$ 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 $\lambda$. 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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BibTeX RIS

Tarik Aougab, Matt Clay, Tawfiq Hamed. 2025-06-23. Subgraph Entropy. https://arxiv.org/abs/2506.18838

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