New Ramsey Bounds from Cyclic Graphs of Prime Order
Calkin, Neil J.
Tovey, Craig A.
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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.