{"paper":{"title":"Two kinds of generalized connectivity of dual cubes","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eddie Cheng, Rong-Xia Hao, Shu-Li Zhao","submitted_at":"2018-03-28T04:57:05Z","abstract_excerpt":"Let $S\\subseteq V(G)$ and $\\kappa_{G}(S)$ denote the maximum number $k$ of edge-disjoint trees $T_{1}, T_{2}, \\cdots, T_{k}$ in $G$ such that $V(T_{i})\\bigcap V(T_{j})=S$ for any $i, j \\in \\{1, 2, \\cdots, k\\}$ and $i\\neq j$. For an integer $r$ with $2\\leq r\\leq n$, the {\\em generalized $r$-connectivity} of a graph $G$ is defined as $\\kappa_{r}(G)= min\\{\\kappa_{G}(S)|S\\subseteq V(G)$ and $|S|=r\\}$. The $r$-component connectivity $c\\kappa_{r}(G)$ of a non-complete graph $G$ is the minimum number of vertices whose deletion results in a graph with at least $r$ components. These two parameters are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10414","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"}