Claims

../

1993_07_01_sidorenko: Sidorenko's 1993 theorem in J. Combin. Theory Ser. B bounds R(K_3, H) by 2m + 1 for every m-edge H without isolated vertices; with the one-edge endpoint R(C_3, K_2) = 3 this determines c_1 = 3.

1994_02_01_goddard_kleitman: Goddard and Kleitman's theorem in Discrete Math. 125 (1994) bounds R(K_3, H) by 2m + 1 for every m-edge H without isolated vertices; with the one-edge endpoint R(C_3, K_2) = 3 this determines c_1 = 3.

2026_06_09_cambie_freschi: Cambie and Freschi's Theorem 3 (preprint of 9 June 2026) bounds R(C_ℓ, H) by (ℓ − 1)m + 1 for every ℓ ≥ 3 and every m-edge H without isolated vertices, giving c_k = 2k + 1 for every k; a disputed, unaccepted full claim.

---