{"paper":{"title":"Extremal problems on saturation for the family of $k$-edge-connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Douglas B. West, Hui Lei, Suil O, Xuding Zhu, Yongtang Shi","submitted_at":"2017-10-20T07:09:13Z","abstract_excerpt":"Let $\\mathcal{F}$ be a family of graphs. A graph $G$ is $\\mathcal{F}$-saturated if $G$ contains no member of $\\mathcal{F}$ as a subgraph but $G+e$ contains some member of $\\mathcal{F}$ whenever $e\\in E(\\overline{G})$. The saturation number and extremal number of $\\mathcal{F}$, denoted $sat(n,\\mathcal{F})$ and $ex(n,\\mathcal{F})$ respectively, are the minimum and maximum numbers of edges among $n$-vertex $\\mathcal{F}$-saturated graphs. For $k\\in\\mathbb{N}$, let $\\mathcal{F}_k$ and $\\mathcal{F}'_k$ be the families of $k$-connected and $k$-edge-connected graphs, respectively. Wenger proved $sat(n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07432","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"}