Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2605.23773 |
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Inhaltsangabe:
- We prove that, among rectangular grid graphs with a fixed number of vertices, the number of spanning trees increases when the side lengths are made more balanced. In particular, among all rectangular grid graphs with $n^2$ vertices, the square $n\times n$ grid has the largest number of spanning trees. The proof starts with the Laplacian product formula, passes to hyperbolic coordinates, and compares logarithms by separating a discrete-concavity term from a positive decreasing residual term.