{"paper":{"title":"On the growth rate of dichromatic numbers of finite subdigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Attila Jo\\'o","submitted_at":"2019-08-20T10:30:26Z","abstract_excerpt":"Chris Lambie-Hanson proved recently that for every function $ f:\\mathbb{N}\\rightarrow \\mathbb{N} $ there is an $ \\aleph_1 $-chromatic graph $ G $ of size $ 2^{\\aleph_1} $ such that every $ (n+3) $-chromatic subgraph of $ G $ has at least $ f(n) $ vertices. Previously, this fact was just known to be consistently true due to P. Komj\\'ath and S. Shelah. We investigate the analogue of this question for directed graphs. In the first part of the paper we give a simple method to construct for an arbitrary $ f:\\mathbb{N}\\rightarrow \\mathbb{N} $ an uncountably dichromatic digraph $ D $ of size $ 2^{\\al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07264","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07264/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"}