{"paper":{"title":"The spectral radius of graphs with no $K_{2,t}$ minor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"V. Nikiforov","submitted_at":"2017-03-06T12:38:11Z","abstract_excerpt":"Let $t\\geq3$ and $G$ be a graph of order $n,$ with no $K_{2,t}$ minor. If $n>400t^{6}$, then the spectral radius $\\mu\\left( G\\right) $ satisfies \\[ \\mu\\left( G\\right) \\leq\\frac{t-1}{2}+\\sqrt{n+\\frac{t^{2}-2t-3}{4}}, \\] with equality if and only if $n\\equiv1$ $(\\operatorname{mod}$ $t)$ and $G=K_{1}\\vee\\left\\lfloor n/t\\right\\rfloor K_{t}$.\n  For $t=3$ the maximum $\\mu\\left( G\\right) $ is found exactly for any $n>40000$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01839","kind":"arxiv","version":1},"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"}