{"paper":{"title":"Temporal Path Covers: Dilworth Properties and Parameterized Complexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aris Pagourtzis, Christos Pergaminelis, Edouard Nemery, Lapo Cioni, Manolis Vasilakis, Sotiris Kanellopoulos","submitted_at":"2026-06-30T19:55:40Z","abstract_excerpt":"The Minimum Temporal Path Cover (TPC) and Minimum Temporally Disjoint Path Cover (TDPC) problems were introduced by [Chakraborty, Dailly, Foucaud, Klasing, MFCS '24]. Both were shown to be NP-hard on temporal DAGs, while the latter is also NP-hard on temporal oriented trees. All tractable cases for T(D)PC established in that paper satisfy a temporal Dilworth property, namely that the size of the minimum T(D)PC is equal to the size of the maximum antichain. This raises a natural question: is T(D)PC polynomial-time solvable under the promise that the respective Dilworth property holds? In this w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00118","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00118/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"}