{"paper":{"title":"The generalized connectivity of some regular graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rong-Xia Hao, Shu-Li Zhao","submitted_at":"2018-08-30T00:44:06Z","abstract_excerpt":"The generalized $k$-connectivity $\\kappa_{k}(G)$ of a graph $G$ is a parameter that can measure the reliability of a network $G$ to connect any $k$ vertices in $G$, which is proved to be NP-complete for a general graph $G$. Let $S\\subseteq V(G)$ and $\\kappa_{G}(S)$ denote the maximum number $r$ of edge-disjoint trees $T_{1}, T_{2}, \\cdots, T_{r}$ in $G$ such that $V(T_{i})\\bigcap V(T_{j})=S$ for any $i, j \\in \\{1, 2, \\cdots, r\\}$ and $i\\neq j$. For an integer $k$ with $2\\leq k\\leq n$, the {\\em generalized $k$-connectivity} of a graph $G$ is defined as $\\kappa_{k}(G)= min\\{\\kappa_{G}(S)|S\\subse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10074","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"}