{"paper":{"title":"Minimal obstructions to $2$-polar cographs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C\\'esar Hern\\'andez-Cruz, Cl\\'audia Linhares Sales, Pavol Hell","submitted_at":"2017-03-10T01:06:08Z","abstract_excerpt":"A graph is a cograph if it is $P_4$-free. A $k$-polar partition of a graph $G$ is a partition of the set of vertices of $G$ into parts $A$ and $B$ such that the subgraph induced by $A$ is a complete multipartite graph with at most $k$ parts, and the subgraph induced by $B$ is a disjoint union of at most $k$ cliques with no other edges.\n  It is known that $k$-polar cographs can be characterized by a finite family of forbidden induced subgraphs, for any fixed $k$. A concrete family of such forbidden induced subgraphs is known for $k=1$, since $1$-polar graphs are precisely split graphs. For larg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03500","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"}