{"paper":{"title":"The saturation number of W 4","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jinze Hu, Ning Song, Qing Cui, Shengjin Ji","submitted_at":"2025-03-14T15:02:42Z","abstract_excerpt":"For a fixed graph $H$, a graph $G$ is called $H$-saturated if $G$ does not contain $H$ as a (not necessarily induced) subgraph, but $G+e$ contains a copy of $H$ for any $e\\in E(\\overline{G})$. The saturation number of $H$, denoted by ${\\rm sat}(n,H)$, is the minimum number of edges in an $n$-vertex $H$-saturated graph. A wheel $W_n$ is a graph obtained from a cycle of length $n$ by adding a new vertex and joining it to every vertex of the cycle. A well-known result of Erd\\H{o}s, Hajnal and Moon shows that ${\\rm sat}(n,W_3)=2n-3$ for all $n\\geq 4$ and $K_2\\vee \\overline{K_{n-2}}$ is the unique "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.11473","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.11473/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}