The bipartite k_2,2-free process and bipartite ramsey number b(2, t)

The bipartite Ramsey number b(s, t) is the smallest integer n such that every blue-red edge coloring of K_n,n contains either a blue K_s,s or a red K_t,t . In the bipartite K_2,2-free process, we begin with an empty graph on vertex set X ∪ Y, |X| = |Y | = n. At each step, a random edge from X × Y is added under the restriction that no K_2,2 is formed. This step is repeated until no more edges can be added. In this note, we analyze this process and prove that the resulting graph shows that b(2, t) = Ω⁽t^3/2/ log t⁾, thereby improving the best known lower bound.