{"paper":{"title":"On 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":"David G. L. Wang, H. L. Lu","submitted_at":"2011-09-22T16:08:21Z","abstract_excerpt":"An $H_n$-factor of a graph $G$ is defined to be a spanning subgraph $F$ of $G$ such that each vertex has degree belonging to the set $\\{1,3,5,...,2n-1,2n\\}$ in $F$. In this paper, we investigate $H_n$-factors of graphs by using Lov\\'asz's structural descriptions to the degree prescribed subgraph problem. We find some sufficient conditions for the existence of an $H_n$-factor of a graph. In particular, we make progress on the characterization problem for a special family of graphs proposed by Cui and Kano in 1988."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4863","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"}