{"paper":{"title":"The generalized 3-connectivity of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ran Gu, Xueliang Li, Yongtang Shi","submitted_at":"2013-03-21T05:40:07Z","abstract_excerpt":"The generalized connectivity of a graph $G$ was introduced by Chartrand et al. Let $S$ be a nonempty set of vertices of $G$, and $\\kappa(S)$ be defined as the largest number of internally disjoint trees $T_1, T_2, \\cdots, T_k$ connecting $S$ in $G$. Then for an integer $r$ with $2 \\leq r \\leq n$, the {\\it generalized $r$-connectivity} $\\kappa_r(G)$ of $G$ is the minimum $\\kappa(S)$ where $S$ runs over all the $r$-subsets of the vertex set of $G$. Obviously, $\\kappa_2(G)=\\kappa(G)$, is the vertex connectivity of $G$, and hence the generalized connectivity is a natural generalization of the vert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5171","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"}