{"paper":{"title":"The complexity of decomposing a graph into a matching and a bounded linear forest","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Adva Mond, Agnijo Banerjee, Jan Petr, Jo\\~ao Pedro Marciano, Julien Portier","submitted_at":"2023-04-06T17:41:53Z","abstract_excerpt":"Deciding whether a graph can be edge-decomposed into a matching and a $k$-bounded linear forest was recently shown by Campbell, H{\\\"o}rsch and Moore to be NP-complete for every $k \\ge 9$, and solvable in polynomial time for $k=1,2$. In the first part of this paper, we close this gap by showing that this problem is in NP-complete for every $k \\ge 3$. In the second part of the paper, we show that deciding whether a graph can be edge-decomposed into a matching and a $k$-bounded star forest is polynomially solvable for any $k \\in \\mathbb{N} \\cup \\{ \\infty \\}$, answering another question by Campbel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.03256","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/2304.03256/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"}