{"paper":{"title":"Sharp spectral bounds for the edge-connectivity of a regular graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hyunju Yu, Jeong Rye Park, Jongyook Park, Suil O","submitted_at":"2018-10-02T12:00:07Z","abstract_excerpt":"Let $\\lambda_2(G)$ and $\\kappa'(G)$ be the second largest eigenvalue and the edge-connectivity of a graph $G$, respectively. Let $d$ be a positive integer at least 3. For $t=1$ or 2, Cioaba proved sharp upper bounds for $\\lambda_2(G)$ in a $d$-regular simple graph $G$ to guarantee that $\\kappa'(G) \\ge t+1$. In this paper, we settle down for all $t \\ge 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01189","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"}