{"paper":{"title":"Average connectivity of minimally 2-connected graphs and average edge-connectivity of minimally 2-edge-connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Mol, Ortrud R. Oellermann, Roc\\'io M. Casablanca","submitted_at":"2018-10-03T21:00:13Z","abstract_excerpt":"Let $G$ be a (multi)graph of order $n$ and let $u,v$ be vertices of $G$. The maximum number of internally disjoint $u$-$v$ paths in $G$ is denoted by $\\kappa_G(u,v)$, and the maximum number of edge-disjoint $u$-$v$ paths in $G$ is denoted by $\\lambda_G (u,v)$. The average connectivity of $G$ is defined by $\\overline{\\kappa}(G)=\\sum_{\\{u,v\\}\\subseteq V(G)} \\kappa_G(u,v)/\\tbinom{n}{2},$ and the average edge-connectivity of $G$ is defined by $\\overline{\\lambda}(G)=\\sum_{\\{u,v\\}\\subseteq V(G)} \\lambda_G(u,v)/\\tbinom{n}{2}$. A graph $G$ is called ideally connected if $\\kappa_G(u,v)=\\min\\{\\mathrm{de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01972","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"}