{"paper":{"title":"Saturation numbers in tripartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eric Sullivan, Paul S. Wenger","submitted_at":"2014-08-25T20:55:20Z","abstract_excerpt":"Given graphs $H$ and $F$, a subgraph $G\\subseteq H$ is an $F$-saturated subgraph of $H$ if $F\\nsubseteq G$, but $F\\subseteq G+e$ for all $e\\in E(H)\\setminus E(G)$. The saturation number of $F$ in $H$, denoted $\\text{sat}(H,F)$, is the minimum number of edges in an $F$-saturated subgraph of $H$. In this paper we study saturation numbers of tripartite graphs in tripartite graphs. For $\\ell\\ge 1$ and $n_1$, $n_2$, and $n_3$ sufficiently large, we determine $\\text{sat}(K_{n_1,n_2,n_3},K_{\\ell,\\ell,\\ell})$ and $\\text{sat}(K_{n_1,n_2,n_3},K_{\\ell,\\ell,\\ell-1})$ exactly and $\\text{sat}(K_{n_1,n_2,n_3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5927","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"}