\(R(C_n,C_n,C_n)\leqq (4+o(1))n\)
Any coloring of ``almost all'' the edges of \(K_{4(1 + \eta)n}\) with three colors yields a monochromatic odd cycle of length at least \((1 + {\eta /10})n\), for every \(0 < \eta <10^{-5}\) and \(n \geq \exp(\eta ^{-50})\). It follows that the Ramsey number \(R(C_n,C_n,C_n)\) is bounded from above by \((4+o(1))n\). If \(n\) is odd, \(R(C_n,C_n,C_n)=(4+o(1))n\).
scientific article; zbMATH DE number 1346892