Abstract
AbstractFor a positive integer r, let G (r) be the smallest N such that, whenever the edges of the Cartesian product KN × KN are r‐colored, then there is a rectangle in which both pairs of opposite edges receive the same color. In this paper, we improve the upper bounds on G (r) by proving , for r large enough. Unlike the previous improvements, which were based on bounds for the size of set systems with restricted intersection sizes, our proof is a form of quasirandomness argument.
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