Zero-One Law for random uniform hypergraphs

Abstract

In this work limit probabilities of first-order properties of the random $s$-uniform hypergraph in the binomial model $G^s(n,p)$ are studied. We give a complete discription of all positive $\alpha$ such that $G^s(n,n^{-\alpha })$ obeys Zero-One Law. Moreover, for any rational $\rho \ge 1/(s-1)$ we prove the existence of a strictly balanced $s$-uniform hypergraph with the density $\rho$.

References in corpus (1)

• Some examples of asymptotic combinatorial behavior, zero-one and convergence results on random hypergraphs