(Georgia Institute of Technology, 1995-09)
Calkin, Neil J.; Erdös, Paul; 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.