{"paper":{"title":"A spectral lower bound for the divisorial gonality of metric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.AG","authors_text":"Janne Kool, Omid Amini","submitted_at":"2014-07-21T19:56:17Z","abstract_excerpt":"Let $\\Gamma$ be a compact metric graph, and denote by $\\Delta$ the Laplace operator on $\\Gamma$ with the first non-trivial eigenvalue $\\lambda_1$. We prove the following Yang-Li-Yau type inequality on divisorial gonality $\\gamma_{div}$ of $\\Gamma$. There is a universal constant $C$ such that \\[\\gamma_{div}(\\Gamma) \\geq C \\frac{\\mu(\\Gamma) . \\ell_{\\min}^{\\mathrm{geo}}(\\Gamma). \\lambda_1(\\Gamma)}{d_{\\max}},\\] where the volume $\\mu(\\Gamma)$ is the total length of the edges in $\\Gamma$, $\\ell_{\\min}^{\\mathrm{geo}}$ is the minimum length of all the geodesic paths between points of $\\Gamma$ of valen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5614","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}