Configurations in projective planes and quadrilateral-star Ramsey numbers

Some classes of configurations in projective planes with polarity are constructed. As the main result, lower bounds for the Ramsey numbers r(n)=r(C4;K1,n)r(n)=r(C4;K1,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(q2-2q+1)=q2-q+1r(q2-2q+1)=q2-q+1 whenever q   is a power of 2. Moreover, the constructions also imply a known result on C4-K1,nC4-K1,n bipartite Ramsey numbers.