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