{"paper":{"title":"Simplified existence theorems on all fractional [a,b]-factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu","submitted_at":"2011-03-21T11:37:04Z","abstract_excerpt":"Let $G$ be a graph with order $n$ and let $g, f : V (G)\\rightarrow N$ such that $g(v)\\leq f(v)$ for all $v\\in V(G)$. We say that $G$ has all fractional $(g, f)$-factors if $G$ has a fractional $p$-factor for every $p: V (G)\\rightarrow N$ such that $g(v)\\leq p(v)\\leq f (v)$ for every $v\\in V(G)$. Let $a<b$ be two positive integers. %and $G$ \\textbf{a graph} of order $n$ sufficiently large %for $a$ and $b$. If $g\\equiv a$, $f\\equiv b$ and $G$ has all fractional $(g,f)$-factors, then we say that $G$ has all fractional $[a,b]$-factors. Suppose that $n$ is sufficiently large for $a$ and $b$.\n  This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3983","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"}