{"paper":{"title":"Stability in Graphs with Matroid Constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Fedor V. Fomin, Petr A. Golovach, Saket Saurabh, Tuukka Korhonen","submitted_at":"2024-04-05T09:21:29Z","abstract_excerpt":"We study the following Independent Stable Set problem. Let G be an undirected graph and M = (V(G),I) be a matroid whose elements are the vertices of G. For an integer k\\geq 1, the task is to decide whether G contains a set S\\subseteq V(G) of size at least k which is independent (stable) in G and independent in M. This problem generalizes several well-studied algorithmic problems, including Rainbow Independent Set, Rainbow Matching, and Bipartite Matching with Separation. We show that\n  - When the matroid M is represented by the independence oracle, then for any computable function f, no algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03979","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/2404.03979/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"}