{"paper":{"title":"An Alternative Proof of the $H$-Factor Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu, Qinglin Yu","submitted_at":"2011-04-27T11:06:19Z","abstract_excerpt":"Let $H: V(G) \\rightarrow 2^{\\mathbb{N}}$ be a set mapping for a graph $G$. Given a spanning subgraph $F$ of $G$, $F$ is called a {\\it general factor} or an $H$-{\\it factor} of $G$ if $d_{F}(x)\\in H(x)$ for every vertex $x\\in V(G)$. $H$-factor problems are, in general, $NP$-complete problems and imply many well-known factor problems (e.g., perfect matchings, $f$-factor problems and $(g, f)$-factor problems) as special cases. Lov\\'asz [The factorization of graphs (II),\n  Acta Math. Hungar., 23 (1972), 223--246] gave a structure description and obtained a deficiency formula for $H$-optimal subgra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5113","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"}