A counter-example to the probabilistic universal graph conjecture via randomized communication complexity

We refute the Probabilistic Universal Graph Conjecture of Harms, Wild, and Zamaraev, which states that a hereditary graph property admits constant-size probabilistic universal if only it is stable has at most factorial speed. Our counter-example follows from existence sequence n×n Boolean matrices Mn, such their public-coin randomized communication complexity tends to infinity, while every submatrix Mn bounded by constant.