Explosive Percolation with Multiple Giant Components
Physical Review Letters, 106 (11):
115701+ (March 2011)DOI: 10.1103/physrevlett.106.115701
Abstract
We generalize the random graph evolution process of Bohman, Frieze, and Wormald T. Bohman, A. Frieze and N. C. Wormald Random Struct. Algorithms 25 432 (2004). Potential edges, sampled uniformly at random from the complete graph, are considered one at a time and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function asymptotically approaching the value α=1/2. We show that multiple giant components appear simultaneously in a strongly discontinuous percolation transition and remain distinct. Furthermore, tuning the value of α determines the number of such components with smaller α leading to an increasingly delayed and more explosive transition. The location of the critical point and strongly discontinuous nature are not affected if only edges which span components are sampled.