{"paper":{"title":"The generalized 3-connectivity of Cartesian product graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hengzhe Li, Xueliang Li, Yuefang Sun","submitted_at":"2011-03-31T06:31:04Z","abstract_excerpt":"The generalized connectivity of a graph, which was introduced recently by Chartrand et al., is a generalization of the concept of vertex connectivity. Let $S$ be a nonempty set of vertices of $G$, a collection $\\{T_1,T_2,...,T_r\\}$ 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 $k$-connectivity $\\kappa_k(G)$ of $G$ is the greatest positive integer $r$ for which $G$ contains at least $r$ internally disjo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6095","kind":"arxiv","version":4},"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"}