{"paper":{"title":"Clique Separator Decomposition of Hole- and Diamond-Free Graphs and Algorithmic Consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Andreas Brandst\\\"adt, Vassilis Giakoumakis","submitted_at":"2011-05-14T08:54:32Z","abstract_excerpt":"Clique separator decomposition introduced by Tarjan and Whitesides is one of the most important graph decompositions. A graph is an {\\em atom} if it has no clique separator. A {\\em hole} is a chordless cycle with at least five vertices, and an {\\em antihole} is the complement graph of a hole. A graph is {\\em weakly chordal} if it is hole- and antihole-free. $K_4-e$ is also called {\\em diamond}. {\\em Paraglider} has five vertices four of which induce a diamond, and the fifth vertex sees exactly the two vertices of degree two in the diamond. In this paper we show that atoms of hole- and diamond-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2874","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"}