{"paper":{"title":"Rainbow Tur\\'an problems for a matching and any other graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D\\'aniel Gerbner, Shujing Miao","submitted_at":"2025-05-20T14:07:43Z","abstract_excerpt":"For a family of graphs $\\cF$, a graph is called $\\cF$-free if it does not contain any member of $\\cF$ as a subgraph. Given a collection of graphs $(G_1,\\ldots,G_t)$ on the same vertex set $V$ of size $n$, a rainbow graph on $V$ is obtained by taking at most one edge from each $G_i$. We say that a collection is rainbow $\\cF$-free if it contains no rainbow copy of any member of $\\cF$. In this paper, we study the maximum values of $min_{i\\in [t]}|E(G_i)|$, $\\sum_{i=1}^{t}|E(G_i)|$ and $\\prod_{i=1}^{t}|E(G_i)|$ among rainbow $\\{F,M_{s+1}\\}$-free collections $(G_1,\\ldots,G_t)$ on $n$ vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14386","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/2505.14386/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"}