{"paper":{"title":"Hypergraphs not containing a tight tree with a bounded trunk ~II: 3-trees with a trunk of size 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Dhruv Mubayi, Jacques Verstra\\\"ete, Tao Jiang, Zolt\\'an F\\\"uredi","submitted_at":"2018-07-18T17:48:00Z","abstract_excerpt":"A tight $r$-tree $T$ is an $r$-uniform hypergraph that has an edge-ordering $e_1, e_2, \\dots, e_t$ such that for each $i\\geq 2$, $e_i$ has a vertex $v_i$ that does not belong to any previous edge and $e_i-v_i$ is contained in $e_j$ for some $j<i$. Kalai conjectured in 1984 that every $n$-vertex $r$-uniform hypergraph with more than $\\frac{t-1}{r}\\binom{n}{r-1}$ edges contains every tight $r$-tree $T$ with $t$ edges.\n  A trunk $T'$ of a tight $r$-tree $T$ is a tight subtree $T'$ of $T$ such that vertices in $V(T)\\setminus V(T')$ are leaves in $T$. Kalai's Conjecture was proved in 1987 for tight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07057","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"}