A sharp threshold of propagation connectivity for mixed random hypergraphs

Abstract

This paper studies the propagation connectivity of a random hypergraph $\mathbb{G}$ containing both 2-edges and 3-hyperedges. We find an exact threshold of the propagation connectivity of $\mathbb{G}$: If $I_{\epsilon,r}<-1$, then $\mathbb{G}$ is not propagation connected with high probability; while if $I_{\epsilon,r}>-1$, then $\mathbb{G}$ is propagation connected with high probability, where $I_{\epsilon,r}$ is a constant dependent on the parameters of 2 and 3-edge probabilities.