{"paper":{"title":"Induced subgraphs of graphs with large chromatic number. VII. Gy\\'arf\\'as' complementation conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Paul Seymour","submitted_at":"2017-01-23T09:06:25Z","abstract_excerpt":"A class of graphs is $\\chi$-bounded if there is a function $f$ such that $\\chi(G)\\le f(\\omega(G))$ for every induced subgraph $G$ of every graph in the class, where $\\chi,\\omega$ denote the chromatic number and clique number of $G$ respectively. In 1987, Gy\\'arf\\'as conjectured that for every $c$, if $\\mathcal{C}$ is a class of graphs such that $\\chi(G)\\le \\omega(G)+c$ for every induced subgraph $G$ of every graph in the class, then the class of complements of members of $\\mathcal{C}$ is $\\chi$-bounded. We prove this conjecture. Indeed, more generally, a class of graphs is $\\chi$-bounded if it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06301","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"}