Packing random graphs and hypergraphs

TL;DR

This paper establishes the approximate threshold for packing two random hypergraphs with edge-disjointness, extending to hypergraphs with different densities and including results for packing a random graph with a fixed graph.

Contribution

It determines the threshold for packing random hypergraphs and extends results to hypergraphs with varying densities and fixed graphs.

Findings

Threshold for packing two random hypergraphs determined

Extension to hypergraphs with different densities

Results for packing a random graph with a fixed graph

Abstract

We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have different densities. In the graph case, we prove a stronger result, on packing a random graph with a fixed graph.