Combinatorics · Oct 6, 2026

Cycle–clique Ramsey numbers

Proves the Erdős–Faudree–Rousseau–Schelp conjecture: R(Cm,Kn)=(m−1)(n−1)+1R(C_m,K_n)=(m-1)(n-1)+1 for every m≥n≥3m\ge n\ge3, except R(C3,K3)=6R(C_3,K_3)=6. This is the exact threshold forcing a red m-cycle or a blue n-clique in every red–blue coloring of a complete graph.

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