{"paper":{"title":"Smaller subgraphs of minimum degree k","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andreas Noever, Frank Mousset, Nemanja \\v{S}kori\\'c","submitted_at":"2017-03-01T12:51:51Z","abstract_excerpt":"In 1990 Erd\\H{o}s, Faudree, Rousseau and Schelp proved that for $k\\geq 2$, every graph with $n\\geq k+1$ vertices and $(k-1)(n-k+2)+\\binom{k-2}{2}+1$ edges contains a subgraph of minimum degree $k$ on at most $n-\\sqrt{n}/\\sqrt{6k^3}$ vertices. They conjectured that it is possible to remove at least $\\epsilon_k n$ many vertices and remain with a subgraph of minimum degree $k$, for some $\\epsilon_k>0$. We make progress towards their conjecture by showing that one can remove at least $\\Omega(n/\\log n)$ many vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00273","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"}