Continuity of the explosive percolation transition

The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent tau = 2.06(2), followed by a hump. We then use the finite-size scaling method to make all the distributions at various system sizes up to N = 2(37) collapse perfectly onto a scaling curve characterized solely by the single exponent tau. We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as N -> infinity. Based on these observations, we show that the explosive percolation transition in the model should be continuous, contrary to the widely spread belief of its discontinuity.