New Ramsey Bounds from Cyclic Graphs of Prime Order

1991 Mathematics Subject Classification. 05D10, 05C80.We present new explicit lower bounds for some Ramsey numbers. All the graphs are cyclic, and are on a prime number of vertices. We give a partial probabilistic analysis which suggests that the cyclic Ramsey numbers grow exponentially. We show that the standard expectation arguments are insu cient to prove such a result. These arguments motivated our searching for Ramsey graphs of prime order