{"paper":{"title":"Hierarchical complexity of 2-clique-colouring weakly chordal graphs and perfect graphs having cliques of size at least 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"Celina M. H. de Figueiredo, H\\'elio B. Mac\\^edo Filho, Raphael C. S. Machado","submitted_at":"2013-12-07T11:11:34Z","abstract_excerpt":"A clique of a graph is a maximal set of vertices of size at least 2 that induces a complete graph. A $k$-clique-colouring of a graph is a colouring of the vertices with at most $k$ colours such that no clique is monochromatic. D\\'efossez proved that the 2-clique-colouring of perfect graphs is a $\\Sigma_2^P$-complete problem [J. Graph Theory 62 (2009) 139--156]. We strengthen this result by showing that it is still $\\Sigma_2^P$-complete for weakly chordal graphs. We then determine a hierarchy of nested subclasses of weakly chordal graphs whereby each graph class is in a distinct complexity clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2086","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"}