Multiplex analogues of Kahn–Kalai threshold conjectures

Investigate the implications of the Kahn–Kalai conjectures for thresholds of global structures in multiplex or colored-graph models.

Background

The paper develops threshold results for fixed-size submultiplexes in the two-layer correlated Erdős–Rényi multiplex model. It notes that analogous threshold questions for large submultiplexes, including spanning structures such as Hamiltonian cycles and perfect matchings, remain a natural direction beyond the fixed-size setting studied in the paper.

The authors specifically suggest examining whether the Kahn–Kalai conjectures, together with the cited recent breakthrough on those conjectures, have implications for threshold phenomena in multiplex or equivalently colored-graph settings. This is included because the passage explicitly refers to the Kahn–Kalai conjectures while proposing their application to the unresolved large-structure threshold problem.