{"paper":{"title":"The Complexity of All $(g,f)$-Factor Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu","submitted_at":"2017-02-20T06:35:24Z","abstract_excerpt":"Let $G$ be a graph with vertex set $V$ and let $g, f : V\\rightarrow \\mathbb{Z}^+$ be two functions such that $g\\le f$. We say that $G$ has all $(g, f )$-factors if $G$ has an $h$-factor for every $h: V\\rightarrow \\mathbb{Z}^+$ such that $g(v)\\le h(v)\\le f (v)$ for every $v\\in V$ and $\\sum_{v\\in{V}}h(v)\\equiv 0\\pmod 2$. Two decades ago, Niessen derived from Tutte's $f$-factor theorem a similar characterization for the property of graphs having all $(g, f )$-factors and asked whether there is a polynomial time algorithm for testing whether a graph $G$ has all $(g, f )$-factors (A characterizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05874","kind":"arxiv","version":2},"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"}