{"paper":{"title":"Clique-Width for Graph Classes Closed under Complementation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Alexandre Blanch\\'e, Dani\\\"el Paulusma, Konrad K. Dabrowski, Matthew Johnson, Vadim V. Lozin, Viktor Zamaraev","submitted_at":"2017-05-22T11:38:41Z","abstract_excerpt":"Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set ${\\cal H}$ of forbidden induced subgraphs. We initiate a systematic study into the boundedness of clique-width of hereditary graph classes closed under complementation. First, we extend the known classification for the $|{\\cal H}|=1$ case by classifying the boundedness of clique-width for every set ${\\cal H}$ of self-complementary graphs. We then completely settle the $|{\\cal H}|=2$ case. In particular, we determ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07681","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"}