{"paper":{"title":"Generalized Tur\\'an problem with bounded matching number","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xinmin Hou, Yue Ma","submitted_at":"2023-01-13T15:51:24Z","abstract_excerpt":"For a graph $T$ and a set of graphs $\\mathcal{H}$, let $\\mbox{ex}(n,T,\\mathcal{H})$ denote the maximum number of copies of $T$ in an $n$-vertex $\\mathcal{H}$-free graph. Recently, Alon and Frankl~(arXiv2210.15076) determined the exact value of $\\mbox{ex}(n,K_2,\\{K_{k+1},M_{s+1}\\})$, where $K_{k+1}$ and $M_{s+1}$ are complete graph on $k+1$ vertices and matching of size $s+1$, respectively. Soon after, Gerbner~(arXiv2211.03272) continued the study by extending $K_{k+1}$ to general fixed graph $H$. In this paper, we continue the study of the function $\\mbox{ex}(n, T,\\{H,M_{s+1}\\})$ when $T=K_r$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.05625","kind":"arxiv","version":2},"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/2301.05625/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"}