{"paper":{"title":"Perfect digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C\\^andida Nunes da Silva, Maycon Sambinelli, Orlando Lee","submitted_at":"2019-04-04T21:45:49Z","abstract_excerpt":"Let $D$ be a digraph. Given a set of vertices $S \\subseteq V(D)$, an $S$-path partition $\\mathcal{P}$ of $D$ is a collection of paths of $D$ such that $\\{V(P) \\colon P \\in \\mathcal{P}\\}$ is a partition of $V(D)$ and $|V(P) \\cap S| = 1$ for every $P \\in \\mathcal{P}$. We say that $D$ satisfies the $\\alpha$-property if, for every maximum stable set $S$ of $D$, there exists an $S$-path partition of $D$, and we say that $D$ is $\\alpha$-diperfect if every induced subdigraph of $D$ satisfies the $\\alpha$-property. A digraph $C$ is an anti-directed odd cycle if (i) the underlying graph of $C$ is a cyc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02799","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"}