title: Percolation transitions in scale-free networks under the Achlioptas process.
abstract: It has been recently shown that the percolation transition is discontinuous in Erdos-Rényi networks and square lattices in two dimensions under the Achlioptas process (AP). Here, we show that when the structure is highly heterogeneous as in scale-free networks, a discontinuous transition does not always occur: a continuous transition is also possible depending on the degree distribution of the scale-free network. This originates from the competition between the AP that discourages the formation of a giant component and the existence of hubs that encourages it. We also estimate the value of the characteristic degree exponent that separates the two transition types.
authors.affiliation: Center for Theoretical Physics and Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
authors.forename: Y S
authors.initials: YS
authors.lastname: Cho
authors.forename: J S
authors.initials: JS
authors.lastname: Kim
authors.forename: J
authors.initials: J
authors.lastname: Park
authors.forename: B
authors.initials: B
authors.lastname: Kahng
authors.forename: D
authors.initials: D
authors.lastname: Kim