{"paper":{"title":"A generalization of Stiebitz-type results on graph decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chunlei Zu, Qinghou Zeng","submitted_at":"2020-09-04T13:19:36Z","abstract_excerpt":"In this paper, we consider the decomposition of multigraphs under minimum degree constraints and give a unified generalization of several results by various researchers. Let $G$ be a multigraph in which no quadrilaterals share edges with triangles and other quadrilaterals and let $\\mu_G(v)=\\max\\{\\mu_G(u,v):u\\in V(G)\\setminus\\{v\\}\\}$, where $\\mu_G(u,v)$ is the number of edges joining $u$ and $v$ in $G$. We show that for any two functions $a,b:V(G)\\rightarrow\\mathbb{N}\\setminus\\{0,1\\}$, if $d_G(v)\\ge a(v)+b(v)+2\\mu_G(v)-3$ for each $v\\in V(G)$, then there is a partition $(X,Y)$ of $V(G)$ such th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02175","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.02175/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}