Sharp threshold functions for the random intersection graph via coupling method?

TL;DR

This paper introduces a new coupling method to determine sharp threshold functions for key properties in random intersection graphs, such as connectivity, perfect matchings, and Hamilton cycles.

Contribution

The paper presents a novel coupling approach that effectively finds threshold functions for various properties in random intersection graphs, advancing the analytical tools available.

Findings

Established sharp threshold functions for k-connectivity

Determined thresholds for perfect matching containment

Identified thresholds for Hamilton cycle containment

Abstract

We will present a new method, which enables us to find threshold functions for many properties in random intersection graphs. This method will be used to establish sharp threshold functions in random intersection graphs for k-connectivity, perfect matching containment and Hamilton cycle containment.