{"paper":{"title":"Spectral radius and Hamiltonian properties of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning, Jun Ge","submitted_at":"2013-09-01T13:06:31Z","abstract_excerpt":"Let $G$ be a graph with minimum degree $\\delta$. The spectral radius of $G$, denoted by $\\rho(G)$, is the largest eigenvalue of the adjacency matrix of $G$. In this note we mainly prove the following two results. (1) Let $G$ be a graph on $n\\geq 4$ vertices with $\\delta\\geq 1$. If $\\rho(G)> n-3$, then $G$ contains a Hamilton path unless $G\\in\\{K_1\\vee (K_{n-3}+2K_1),K_2\\vee 4K_1,K_1\\vee (K_{1,3}+K_1)\\}$. (2) Let $G$ be a graph on $n\\geq 14$ vertices with $\\delta \\geq 2$. If $\\rho(G)\\geq \\rho(K_2\\vee (K_{n-4}+2K_1))$, then $G$ contains a Hamilton cycle unless $G= K_2\\vee (K_{n-4}+2K_1)$. As cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0217","kind":"arxiv","version":6},"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"}