{"paper":{"title":"Characterizations of minimal graphs with equal edge connectivity and spanning tree packing number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong-Jian Lai, Ping Li, Senmei Yao, Xiaofeng Gu","submitted_at":"2014-10-20T22:13:18Z","abstract_excerpt":"With graphs considered as natural models for many network design problems, edge connectivity $\\kappa'(G)$ and maximum number of edge-disjoint spanning trees $\\tau(G)$ of a graph $G$ have been used as measures for reliability and strength in communication networks modeled as graph $G$ (see \\cite{Cunn85, Matula87}, among others). Mader \\cite{Mader71} and Matula \\cite{Matula72} introduced the maximum subgraph edge connectivity $\\overline{\\kappa'}(G)=\\max \\{\\kappa'(H): H \\mbox{ is a subgraph of } G \\}$. Motivated by their applications in network design and by the established inequalities \\[ \\overl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5486","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"}