{"paper":{"title":"Deciding k-colourability of $P_5$-free graphs in polynomial time","license":"","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ch\\'inh T. Ho\\`ang, J. Sawada, Marcin Kami\\'nski, Vadim Lozin, X. Shu","submitted_at":"2007-02-07T15:29:32Z","abstract_excerpt":"The problem of computing the chromatic number of a $P_5$-free graph is known to be NP-hard. In contrast to this negative result, we show that determining whether or not a $P_5$-free graph admits a $k$-colouring, for each fixed number of colours $k$, can be done in polynomial time. If such a colouring exists, our algorithm produces it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0702043","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"}