{"paper":{"title":"On extremal graphs with at most $\\ell$ internally disjoint Steiner trees connecting any n-1 vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xueliang Li, Yaping Mao","submitted_at":"2013-04-13T04:23:23Z","abstract_excerpt":"The concept of maximum local connectivity $\\bar {\\kappa}$ of a graph was introduced by Bollob\\'{a}s. One of the problems about it is to determine the largest number of edges $f(n;\\bar{\\kappa}\\leq \\ell)$ for graphs of order $n$ that have local connectivity at most $\\ell$. We consider a generalization of the above concept and problem. For $S\\subseteq V(G)$ and $|S|\\geq 2$, the \\emph{generalized local connectivity} $\\kappa(S)$ is the maximum number of internally disjoint trees connecting $S$ in $G$. The parameter $\\bar{\\kappa}_k(G)=max\\{\\kappa(S)|S\\subseteq V(G),|S|=k\\}$ is called the \\emph{maxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3774","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"}