{"paper":{"title":"Vertex Tur\\'an problems for the oriented hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Bal\\'azs Patk\\'os, D\\'aniel Gerbner, D\\'aniel T. Nagy, M\\'at\\'e Vizer","submitted_at":"2018-07-18T11:13:37Z","abstract_excerpt":"In this short note we consider the oriented vertex Tur\\'an problem in the hypercube: for a fixed oriented graph $\\overrightarrow{F}$, determine the maximum size $ex_v(\\overrightarrow{F}, \\overrightarrow{Q_n})$ of a subset $U$ of the vertices of the oriented hypercube $\\overrightarrow{Q_n}$ such that the induced subgraph $\\overrightarrow{Q_n}[U]$ does not contain any copy of $\\overrightarrow{F}$. We obtain the exact value of $ex_v(\\overrightarrow{P_k}, \\overrightarrow{Q_n})$ for the directed path $\\overrightarrow{P_k}$, the exact value of $ex_v(\\overrightarrow{V_2}, \\overrightarrow{Q_n})$ for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06866","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"}