{"paper":{"title":"The chromatic number of finite type-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bill Kay, Christian Avart, Christian Reiher, Vojt\\v{e}ch R\\\"odl","submitted_at":"2016-03-16T14:56:41Z","abstract_excerpt":"By a finite type-graph we mean a graph whose set of vertices is the set of all $k$-subsets of $[n]=\\{1,2,\\ldots, n\\}$ for some integers $n\\ge k\\ge 1$, and in which two such sets are adjacent if and only if they realise a certain order type specified in advance. Examples of such graphs have been investigated in a great variety of contexts in the literature with particular attention being paid to their chromatic number. In recent joint work with Tomasz {\\L}uczak, two of the authors embarked on a systematic study of the chromatic numbers of such type-graphs, formulated a general conjecture determ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05134","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"}