{"paper":{"title":"A proof of a conjecture of Erd\\H{o}s, Faudree, Rousseau and Schelp on subgraphs of minimum degree $k$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lisa Sauermann","submitted_at":"2017-05-28T19:24:57Z","abstract_excerpt":"Erd\\H{o}s, Faudree, Rousseau and Schelp observed the following fact for every fixed integer $k\\geq 2$: Every graph on $n\\geq k-1$ vertices with at least $(k-1)(n-k+2)+{k-2\\choose 2}$ edges contains a subgraph with minimum degree at least $k$. However, there are examples in which the whole graph is the only such subgraph. Erd\\H{o}s et al. conjectured that having just one more edge implies the existence of a subgraph on at most $(1-\\varepsilon_k)n$ vertices with minimum degree at least $k$, where $\\varepsilon_k>0$ depends only on $k$. We prove this conjecture, using and extending ideas of Mousse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09979","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"}