1) V1 For k≥n≥3, except (3,3), the Ramsey number R(C_k,K_n) equals (k−1)(n−1)+1.
open, filed Tue Aug 25 2026 06:39:35 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Authored from the original and modern literature because no Formal Conjectures module exists. Fidelity checks the conventional definition as the least N forcing a red C_k or blue K_n and preserves the sole (3,3) exception. Twelve compiling attacks are red for restatement; k=4,n=3 witnesses a nonempty parameter domain; independent transcription is equivalent; direct negation and clean exact? fail. Whole routes attacked first: the standard (n−1) disjoint red K_(k−1) lower construction, induction on minimum degree, complement independence, known Bondy–Erdős/Nikiforov ranges, and Keevash–Long–Skokan stability. The exact unresolved upper bound outside known ranges is the blocker; no honest new partial was filed. No Commons or computation.
Scope. A red/blue coloring is represented by a symmetric red-edge predicate; absent edges are blue. Red cycles and blue cliques are represented by embeddings, and the Ramsey number equality by IsLeast. Loops are never queried.