{"paper":{"title":"On Edge-Colored Saturation Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Schulte, Casey Tompkins, Daniel Johnston, Eric Sullivan, Florian Pfender, Heather C. Smith, Michael Ferrara, Michael Tait, Sarah Loeb","submitted_at":"2017-12-01T02:28:29Z","abstract_excerpt":"Let $\\mathcal{C}$ be a family of edge-colored graphs. A $t$-edge colored graph $G$ is $(\\mathcal{C}, t)$-saturated if $G$ does not contain any graph in $\\mathcal{C}$ but the addition of any edge in any color in $[t]$ creates a copy of some graph in $\\mathcal{C}$. Similarly to classical saturation functions, define $\\mathrm{sat}_t(n, \\mathcal{C})$ to be the minimum number of edges in a $(\\mathcal{C},t)$ saturated graph. Let $\\mathcal{C}_r(H)$ be the family consisting of every edge-colored copy of $H$ which uses exactly $r$ colors.\n  In this paper we consider a variety of colored saturation prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00163","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"}