Explosive Percolation in Random Networks

Focusing on the Bohman-Frieze-Wormald percolation model, this thesis explores its unique discontinuous transition at the critical threshold, contrasting it with the expected continuous phase transitions in random networks. It delves into the mechanisms behind this phenomenon, uncovering critical behaviors like multiple giant components and phase transitions, as well as unstable giant components. The insights gained are significant for applications across various fields, including physics, chemistry, and biology.