{"paper":{"title":"Colouring perfect graphs with bounded clique number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Aur\\'elie Lagoutte, Maria Chudnovsky, Paul Seymour, Sophie Spirkl","submitted_at":"2017-07-12T14:56:22Z","abstract_excerpt":"A graph is perfect if the chromatic number of every induced subgraph equals the size of its largest clique, and an algorithm of Gr\\\"otschel, Lov\\'asz, and Schrijver from 1988 finds an optimal colouring of a perfect graph in polynomial time. But this algorithm uses the ellipsoid method, and it is a well-known open question to construct a \"combinatorial\" polynomial-time algorithm that yields an optimal colouring of a perfect graph.\n  A skew partition in $G$ is a partition $(A,B)$ of $V(G)$ such that $G[A]$ is not connected and $\\bar{G}[B]$ is not connected, where $\\bar{G}$ denotes the complement"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03747","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"}