{"paper":{"title":"Extremal problems for a matching and any other graph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiutao Zhu, Yaojun Chen","submitted_at":"2023-07-22T05:23:57Z","abstract_excerpt":"For a family of graphs $\\F$, a graph is called $\\F$-free if it does not contain any member of $\\F$ as a subgraph. The generalized Tur\\'an number $\\ex(n,K_r,\\F)$ is the maximum number of $K_r$ in an $n$-vertex $\\F$-free graph and $\\ex(n,K_2,\\F)=\\ex(n,\\F)$, i.e., the classical Tur\\'an number. Let $M_{s+1}$ be a matching on $s+1$ edges and $F$ be any graph. In this paper, we determine $\\ex(n,K_r, \\{M_{s+1},F\\})$ apart from a constant additive term and also give a condition when the error constant term can be determined. In particular, we give the exact value of $\\ex(n,\\{M_{s+1},F\\})$ for $F$ bein"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.11983","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/2307.11983/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"}