{"paper":{"title":"On the Tur\\'an number of ordered forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Weidert, D\\'aniel Kor\\'andi, G\\'abor Tardos, Istv\\'an Tomon","submitted_at":"2017-11-21T11:25:46Z","abstract_excerpt":"An ordered graph $H$ is a simple graph with a linear order on its vertex set. The corresponding Tur\\'an problem, first studied by Pach and Tardos, asks for the maximum number $\\text{ex}_<(n,H)$ of edges in an ordered graph on $n$ vertices that does not contain $H$ as an ordered subgraph. It is known that $\\text{ex}_<(n,H) > n^{1+\\varepsilon}$ for some positive $\\varepsilon=\\varepsilon(H)$ unless $H$ is a forest that has a proper 2-coloring with one color class totally preceding the other one. Making progress towards a conjecture of Pach and Tardos, we prove that $\\text{ex}_<(n,H) =n^{1+o(1)}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07723","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"}