Examines metric entropy and its implications in graph theory, suggesting new insights.
Given , we prove that there exists depending only on so that if is a metric graph of rank with metric 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.
No takes yet. Share an insight, caveat, or question.
Hamed et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: