Abstract

Some classes of configurations in projective planes with polarity are constructed. As the main result, lower bounds for the Ramsey numbers r ( n ) = r ( C 4 ; K 1 , n ) are derived from these geometric structures, which improve some bounds due to Parsons about 30 years ago, and also yield a new class of optimal values: r ( q 2 - 2 q + 1 ) = q 2 - q + 1 whenever q is a power of 2. Moreover, the constructions also imply a known result on C 4 - K 1 , n bipartite Ramsey numbers.

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