{"paper":{"title":"Spectral radius and Hamiltonicity of graphs with large minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vladimir Nikiforov","submitted_at":"2016-02-02T18:19:21Z","abstract_excerpt":"This paper presents sufficient conditions for Hamiltonian paths and cycles in graphs. Letting $\\lambda\\left( G\\right) $ denote the spectral radius of the adjacency matrix of a graph $G,$ the main results of the paper are:\n  (1) Let $k\\geq1,$ $n\\geq k^{3}/2+k+4,$ and let $G$ be a graph of order $n$, with minimum degree $\\delta\\left( G\\right) \\geq k.$ If \\[ \\lambda\\left( G\\right) \\geq n-k-1, \\] then $G$ has a Hamiltonian cycle, unless $G=K_{1}\\vee(K_{n-k-1}+K_{k})$ or $G=K_{k}\\vee(K_{n-2k}+\\overline{K}_{k})$.\n  (2) Let $k\\geq1,$ $n\\geq k^{3}/2+k^{2}/2+k+5,$ and let $G$ be a graph of order $n$, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01033","kind":"arxiv","version":3},"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"}