{"paper":{"title":"Connected greedy colourings of perfect graphs and other classes: the good, the bad and the ugly","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Aur\\'elie Lagoutte, Caroline Brosse, Florent Foucaud, Laurent Beaudou, Lucas Pastor, Oscar Defrain, Vincent Limouzy","submitted_at":"2021-10-26T20:14:31Z","abstract_excerpt":"The Grundy number of a graph is the maximum number of colours used by the \"First-Fit\" greedy colouring algorithm over all vertex orderings. Given a vertex ordering $\\sigma= v_1,\\dots,v_n$, the \"First-Fit\" greedy colouring algorithm colours the vertices in the order of $\\sigma$ by assigning to each vertex the smallest colour unused in its neighbourhood.\n  By restricting this procedure to vertex orderings that are connected, we obtain {\\em connected greedy colourings}. For some graphs, all connected greedy colourings use exactly $\\chi(G)$ colours; they are called {\\em good graphs}. On the opposi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14003","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.14003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}