{"paper":{"title":"The Tur\\'an problem for a family of tight linear forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jian Wang, Weihua Yang","submitted_at":"2018-12-05T12:05:39Z","abstract_excerpt":"Let $\\mathcal{F}$ be a family of $r$-graphs. The Tur\\'an number $ex_r(n;\\mathcal{F})$ is defined to be the maximum number of edges in an $r$-graph of order $n$ that is $\\mathcal{F}$-free. The famous Erd\\H{o}s Matching Conjecture shows that \\[ ex_r(n,M_{k+1}^{(r)})= \\max\\left\\{\\binom{rk+r-1}{r},\\binom{n}{r}-\\binom{n-k}{r}\\right\\}, \\] where $M_{k+1}^{(r)}$ represents the $r$-graph consisting of $k+1$ disjoint edges. Motivated by this conjecture, we consider the Tur\\'an problem for tight linear forests. A tight linear forest is an $r$-graph whose connected components are all tight paths or isolat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01940","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":""},"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"}