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June 3, 2026Bulletin of the London Mathematical Society0 citationsOpen Access

Subgraph entropy

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THTawfiq HamedBirzeit UniversityTATarik AougabHaverford CollegeMCMatt ClayUniversity of Arkansas at Fayetteville

Key Points

  • The research aims to establish a relationship between metric entropy and the existence of subgraphs in metric graphs.
  • Proved the existence of a specific subgraph depending on the rank of the original graph.
  • Applied concepts from hyperbolic geometry and graph theory to interpret results.
  • Explored connections with the pressure metric on Culler–Vogtmann Outer Space.
  • Identified a proper subgraph with metric entropy at least depending on the original graph's properties.
  • Answered a previously posed question regarding graph metrics and their implications.
  • Established parallels between graph theory and hyperbolic geometry involving the Bers Lemma.

Abstract

Abstract 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.

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Cite This Study

Hamed et al. (2026) studied this question.

synapsesocial.com/papers/6a1fc756dee9eb8c0dce8390https://doi.org/10.1112/blms.70397
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