{"paper":{"title":"Tur\\'an numbers of hypergraph trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tao Jiang, Zolt\\'an F\\\"uredi","submitted_at":"2015-05-13T01:36:19Z","abstract_excerpt":"An $r$-graph is an $r$-uniform hypergraph tree (or $r$-tree) if its edges can be ordered as $E_1,\\ldots, E_m$ such that $\\forall i>1 \\, \\exists \\alpha(i)<i$ such that $E_i\\cap (\\bigcup_{j=1}^{i-1} E_j)\\subseteq E_{\\alpha(i)}$. The Tur\\'an number $ex(n,{\\cal H})$ of an $r$-graph ${\\cal H}$ is the largest size of an $n$-vertex $r$-graph that does not contain ${\\cal H}$. A cross-cut of ${\\cal H}$ is a set of vertices in ${\\cal H}$ that contains exactly one vertex of each edge of ${\\cal H}$. The cross-cut number $\\sigma({\\cal H})$ of ${\\cal H}$ is the minimum size of a cross-cut of ${\\cal H}$. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03210","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"}