{"paper":{"title":"Acyclic orientations with degree constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi, Zolt\\'an Kir\\'aly","submitted_at":"2018-06-09T07:15:32Z","abstract_excerpt":"In this note we study the complexity of some generalizations of the notion of $st$-numbering.\n  Suppose that given some functions $f$ and $g$, we want to order the vertices of a graph such that every vertex $v$ is preceded by at least $f(v)$ of its neighbors and succeeded by at least $g(v)$ of its neighbors.\n  We prove that this problem is solvable in polynomial time if $fg\\equiv 0$, but it becomes NP-complete for $f\\equiv g \\equiv 2$.\n  This answers a question of the first author posed in 2009."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03426","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"}