{"paper":{"title":"Redundant edges in Ramsey graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yan Li, Ye Wang, Yusheng Li","submitted_at":"2017-12-08T03:34:12Z","abstract_excerpt":"For graphs $G$, $F$ and $H$, let $G\\rightarrow (F,H)$ signify that any edge coloring of $G$ in red and blue contains a red $F$ or a blue $H$. The Ramsey number $R(F,H)=\\min\\{r|\\; K_r\\rightarrow (F,H)\\}$. In this note, we consider redundant edges in Ramsey graphs, which are associate with critical Ramsey numbers. For an integer $k\\ge 1$, let ${\\mathbb G}=\\{G_k,G_{k+1},\\dots \\}$ be a class of graphs with $\\delta(G_n)\\ge 1$. We define the critical Ramsey number $R_{\\mathbb G}(F,H)$ with respect to $\\mathbb G$ to be $\\max\\{n|\\; K_r\\setminus G_n \\rightarrow(F,H),\\,G_n\\in{\\mathbb G}\\big\\}$, where $r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03226","kind":"arxiv","version":5},"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"}