{"paper":{"title":"Edge Connectivity, Packing Spanning Trees, and Eigenvalues of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cunxiang Duan, Ligong Wang, Xiangxiang Liu","submitted_at":"2017-04-20T03:38:06Z","abstract_excerpt":"Let $\\mathcal{G}$ be the set of simple graphs (or multigraphs) $G$ such that for each $G \\in \\mathcal{G}$ there exists at least two non-empty disjoint proper subsets $V_{1},V_{2}\\subseteq V(G)$ satisfying $V(G)\\setminus(V_{1} \\cup V_{2})\\neq \\phi$ and edge connectivity $\\kappa'(G)=e(V_{i},V(G)\\backslash V_{i})$ for $1\\leq i \\leq 2$. A multigraph is a graph with possible multiple edges, but no loops. Let $\\tau(G)$ be the maximum number of edge-disjoint spanning trees of a graph $G$. Motivated by a question of Seymour on the relationship between eigenvalues of a graph $G$ and bounds of $\\tau(G)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05994","kind":"arxiv","version":3},"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"}