{"paper":{"title":"A note on eigenvalues and Hamiltoinan properties of $k$-connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong-Jian Lai, Huicai Jia, Ruifang Liu","submitted_at":"2018-09-04T20:01:08Z","abstract_excerpt":"Let $\\lambda_{1}(G)$ and $\\mu_{1}(G)$ denote the spectral radius and the Laplacian spectral radius of a graph $G$, respectively. Li in [Electronic J. Linear Algebra 34 (2018) 389-392] proved sharp upper bounds of $\\lambda_{1}(G)$ based on the connectivity to assure a connected graph to be Hamiltonian and traceable, respectively. In this paper, we present best possible upper bounds of $\\lambda_{1}(G)$ for $k$-connected graphs to be Hamiltonian-connected and homogeneously traceable, respectively. Furthermore, best possible upper bounds of $\\mu_{1}(G)$ to predict $k$-connected graphs to be Hamilt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01227","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"}