{"paper":{"title":"Graph Saturation in Multipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florian Pfender, Michael Ferrara, Michael S. Jacobson, Paul S. Wenger","submitted_at":"2014-08-13T20:31:10Z","abstract_excerpt":"Let $G$ be a fixed graph and let ${\\mathcal F}$ be a family of graphs. A subgraph $J$ of $G$ is ${\\mathcal F}$-saturated if no member of ${\\mathcal F}$ is a subgraph of $J$, but for any edge $e$ in $E(G)-E(J)$, some element of ${\\mathcal F}$ is a subgraph of $J+e$. We let $\\text{ex}({\\mathcal F},G)$ and $\\text{sat}({\\mathcal F},G)$ denote the maximum and minimum size of an ${\\mathcal F}$-saturated subgraph of $G$, respectively. If no element of ${\\mathcal F}$ is a subgraph of $G$, then $\\text{sat}({\\mathcal F},G) = \\text{ex}({\\mathcal F}, G) = |E(G)|$.\n  In this paper, for $k\\ge 3$ and $n\\ge 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3137","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"}