{"paper":{"title":"Orientations of graphs omitting non-edge-critical directed graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hannah Sheats","submitted_at":"2025-02-28T18:10:13Z","abstract_excerpt":"In 1974, Erd\\H{o}s asked the following question: given a graph $G$ and a directed graph $\\vec{H}$, how many ways are there to orient the edges of $G$ such that it does not contain $\\vec{H}$ as a subgraph? We denote this value by $D(G, \\vec{H})$. Further, we let $D(n, \\vec{H})$ denote the maximum of $D(G, \\vec{H})$ over all graphs $G$ on $n$ vertices. In 2006, Alon and Yuster gave an exact answer when $\\vec{H}$ is a tournament. In 2023, Buci\\'c, Janzer, and Sudakov gave asymptotic answers for all directed graphs $\\vec{H}$, and in the same paper, they gave an exact answer when $\\vec{H}$ is a dir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.21287","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.21287/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}