We refute the Probabilistic Universal Graph Conjecture of Harms, Wild, and Zamaraev, which states that a hereditary graph property admits a constant-size probabilistic universal graph if and only if it is stable and has at most factorial speed. Our counter-example follows from the existence of a sequence of $n \times n$ Boolean matrices $M_n$, such that their public-coin randomized communication complexity tends to infinity, while the randomized communication complexity of every $n^{1/4}\times n^{1/4}$ submatrix of $M_n$ is bounded by a universal constant.
翻译:我们驳斥了“伤害、野和扎马拉耶夫”的概率通用图假设,该预测指出,遗传图属性如果并且只有在稳定并且具有最大系数速度的情况下,才会接受一个不变大小的概率通用图。 我们的反实例来自一个波林基体的序列,即$n\ times n$ bollean basm $M_n$,因此其公共-coin随机通信复杂程度往往无限,而每兆元的随机通信复杂程度则受一个通用常数所约束。