Lower Bounds for Multi-Colored Ramsey Numbers From Group Orbits

Abstract

In this paper, the algorithm developed in $[RK]$ for $2$-color Ramsey numbers is generalized to multi-colored Ramsey numbers. All the cyclic graphs yielding the lower bounds $R(3,3,4)\ge 30$, $R(3,3,5)\ge 45$, and $R(3,4,4)\ge 55$ were obtained. The two last bounds are apparently new.