Explosive Percolation Via Control of the Largest Cluster

We disclose that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our novel models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that, surprisingly, the cluster perimeters are fractal at the transition point yielding a fractal dimension of 1.23±0.03 intriguingly close to that of watersheds