{"paper":{"title":"Out-degree reducing partitions of digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Anders Yeo, Fr\\'ed\\'eric Havet, Joergen Bang-Jensen, St\\'ephane Bessy","submitted_at":"2017-07-28T17:45:33Z","abstract_excerpt":"Let $k$ be a fixed integer. We determine the complexity of finding a $p$-partition $(V_1, \\dots, V_p)$ of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by $V_i$, ($1\\leq i\\leq p$) is at least $k$ smaller than the maximum out-degree of $D$. We show that this problem is polynomial-time solvable when $p\\geq 2k$ and ${\\cal NP}$-complete otherwise. The result for $k=1$ and $p=2$ answers a question posed in \\cite{bangTCS636}. We also determine, for all fixed non-negative integers $k_1,k_2,p$, the complexity of deciding whether a given digraph of m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09349","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"}