A new route to Explosive Percolation

The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the cluster sizes unlike the power law distribution in AP In this model single edges between pairs of clusters of sizes s(i) and s(j) are occupied with a probability proportional to (s(i)s(j))(alpha) The parameter alpha is continuously tunable over the entire real axis Numerical studies indicate that for alpha < alpha(c), the transition is first order alpha(c) = 0 for a square lattice and alpha(c) = -1/2 for random graphs In the limits of alpha = -infinity + infinity this model coincides with models well established in the literature (C) 2010 Elsevier B V All rights reserved