{"paper":{"title":"On extremal graphs with at most two internally disjoint Steiner trees connecting any three vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hengzhe Li, Xueliang Li, Yaping Mao","submitted_at":"2012-10-30T14:24:49Z","abstract_excerpt":"The problem of determining the smallest number of edges, $h(n;\\bar{\\kappa}\\geq r)$, which guarantees that any graph with $n$ vertices and $h(n;\\bar{\\kappa}\\geq r)$ edges will contain a pair of vertices joined by $r$ internally disjoint paths was posed by Erd\\\"{o}s and Gallai. Bollob\\'{a}s considered the problem of determining the largest number of edges $f(n;\\bar{\\kappa}\\leq \\ell)$ for graphs with $n$ vertices and local connectivity at most $\\ell$. One can see that $f(n;\\bar{\\kappa}\\leq \\ell)= h(n;\\bar{\\kappa}\\geq \\ell+1)-1$. These two problems had received a wide attention of many researchers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8021","kind":"arxiv","version":2},"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"}