{"paper":{"title":"Ordered and convex geometric trees with linear extremal function","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, Zolt\\'an F\\\"uredi","submitted_at":"2018-12-14T01:01:01Z","abstract_excerpt":"The extremal functions $ex_{\\rightarrow}(n,F)$ and $ex_{\\cir}(n,F)$ for ordered and convex geometric acyclic graphs $F$ have been extensively investigated by a number of researchers. Basic questions are to determine when $ex_{\\rightarrow}(n,F)$ and $ex_{\\cir}(n,F)$ are linear in $n$, the latter posed by Bra\\ss-K\\'arolyi-Valtr in 2003. In this paper, we answer both these questions for every tree $F$.\n  We give a forbidden subgraph characterization for a family $\\cal T$ of ordered trees with $k$ edges, and show that $ex_{\\rightarrow}(n,T) = (k - 1)n - {k \\choose 2}$ for all $n \\geq k + 1$ when $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05750","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"}