{"paper":{"title":"A Degree Condition for a Graph to have $(a,b)$-Parity Factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Haodong Liu, Hongliang Lu","submitted_at":"2016-06-15T01:23:52Z","abstract_excerpt":"Let $a,b,n$ be three positive integers such that $a\\equiv b\\pmod 2$ and $n\\geq b(a+b)(a+b+2)/(2a)$. Let $G$ be a graph of order $n$ with minimum degree at least $a+b/a-1$. We show that $G$ has an $(a,b)$-parity factor, if $max\\{d_G(u),d_G(v)\\}\\geq \\frac{an}{a+b}$ for any two nonadjacent vertices $u,v$ of $G$. It is an extension of Nishimura's results for the existence of $k$-factors (\\emph{J. Graph Theory}, \\textbf{16} (1992), 141--151) and generalizes Li and Cai's result in some senses (\\emph{J. Graph Theory}, \\textbf{27} (1998), 1--6). These conditions are tight."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04608","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"}