{"paper":{"title":"Perfect divisibility and perfect-Pollyanna in bull-free graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Di Wu, Junran Yu, Paras Vinubhai Maniya, Ran Chen","submitted_at":"2026-03-23T03:46:17Z","abstract_excerpt":"A graph $G$ is {\\em perfectly divisible} if, for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $\\omega(H[B])<\\omega(H)$. A {\\em bull} is a graph consisting of a triangle with two disjoint pendant edges. Ho\\`ang [Discrete Math. 349 (2026) 114809] proposed four conjectures: 1. $P_5$-free graphs are perfectly divisible; 2. Odd hole-free graphs are perfectly divisible; 3. Even hole-free graphs are perfectly divisible; and 4. $4K_1$-free graphs are perfectly divisible. Karthick et al. [Electron. J. Combin. 29 (2022) P3.19] proposed a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.21538","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.21538/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}