On the Turán Number of the Cartesian Product of Two Stars

Abstract

We study the Turán number of the Cartesian product of two stars, a family whose order of magnitude is known. For most pairs of star sizes, we determine the leading coefficient exactly. In the remaining congruence class, we give explicit lower and upper bounds for the coefficient at the leading scale. Our lower bounds use blowups of polarity graphs, and our upper bounds use structural estimates on neighbourhoods.