{"paper":{"title":"Complements of nearly perfect graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andr\\'as Gy\\'arf\\'as, Andr\\'as Sebo, Nicolas Trotignon, Raphael Machado, St\\'ephan Thomass\\'e, Zhentao Li","submitted_at":"2013-04-10T07:28:56Z","abstract_excerpt":"A class of graphs closed under taking induced subgraphs is $\\chi$-bounded if there exists a function $f$ such that for all graphs $G$ in the class, $\\chi(G) \\leq f(\\omega(G))$. We consider the following question initially studied in [A. Gy{\\'a}rf{\\'a}s, Problems from the world surrounding perfect graphs, {\\em Zastowania Matematyki Applicationes Mathematicae}, 19:413--441, 1987]. For a $\\chi$-bounded class $\\cal C$, is the class $\\bar{C}$ $\\chi$-bounded (where $\\bar{\\cal C}$ is the class of graphs formed by the complements of graphs from $\\cal C$)? We show that if $\\cal C$ is $\\chi$-bounded by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2862","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"}