{"paper":{"title":"Graphs with large generalized 3-connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hengzhe Li, Xueliang Li, Yaping Mao, Yuefang Sun","submitted_at":"2012-01-14T03:39:01Z","abstract_excerpt":"Let $S$ be a nonempty set of vertices of a connected graph $G$. A collection $T_1,..., T_\\ell$ of trees in $G$ is said to be internally disjoint trees connecting $S$ if $E(T_i)\\cap E(T_j)= \\emptyset$ and $V(T_i)\\cap V(T_j)=S$ for any pair of distinct integers $i, j$, where $1 \\leq i, j \\leq r$. For an integer $k$ with $2 \\leq k \\leq n$, the generalized $k$-connectivity $\\kappa_k(G)$ of $G$ is the greatest positive integer $r$ such that $G$ contains at least $r$ internally disjoint trees connecting $S$ for any set $S$ of $k$ vertices of $G$. Obviously, $\\kappa_2(G)$ is the connectivity of $G$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2983","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"}