{"paper":{"title":"An Extension of Cui-Kano's Characterization Problem on Graph Factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu","submitted_at":"2013-01-20T13:35:02Z","abstract_excerpt":"Let $G$ be a graph with vertex set $V(G)$ and let $H:V(G)\\rightarrow 2^N$ be a set function associating with $G$. An $H$-factor of graph $G$ is a spanning subgraphs $F$ such that $$d_F(v)\\in H(v){4em}\\hbox{for every}v\\in V(G).$$ Let $f:V(G)\\rightarrow N$ be an even integer-valued function such that $f\\geq 4$ and let $H_f(v)=\\{1,3,...,f(v)-1, f(v)\\}$ for $v\\in V(G)$. In this paper, we investigate $H_f$-factors of graphs $G$ by using Lov\\'asz's structural descriptions. Let $o(G)$ denote the number of odd components of $G$.\n  We show that if one of the following conditions holds, then $G$ contain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4657","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"}