{"paper":{"title":"Partitions of multigraphs under degree constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Stiebitz, Thomas Schweser","submitted_at":"2017-03-24T16:53:14Z","abstract_excerpt":"In 1996, Michael Stiebitz proved that if $G$ is a simple graph with $\\delta(G)\\geq s+t+1$ and $s,t\\in \\mathbb{Z}_{\\geq 0}$, then $V(G)$ can be partitioned into two sets $A$ and $B$ such that $\\delta(G[A])\\geq s$ and $\\delta(G[B])\\geq t$. In 2016, Amir Ban proved a similar result for weighted graphs. Let $G$ be a simple graph with at least two vertices, let $w:E(G) \\to \\mathbb{r}_{>0}$ be a weight function, let $s,t \\in \\mathbb{R}_{\\geq 0}$, and let $W=\\max_{e\\in E(G)} w(e)$. If $\\delta(G)\\geq s+t+2W$, then $V(G)$ can be partitioned into two sets $A$ and $B$ such that $\\delta(G[A])\\geq s$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08502","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"}