Computer Science – Discrete Mathematics
Scientific paper
2011-04-07
Computer Science
Discrete Mathematics
Scientific paper
The evolution of the largest component has been studied intensely in a variety of random graph processes, starting in 1960 with the Erd\"os-R\'enyi process. It is well known that this process undergoes a phase transition at n/2 edges when, asymptotically almost surely, a linear-sized component appears. Moreover, this phase transition is continuous, i.e., in the limit the function f(c) denoting the fraction of vertices in the largest component in the process after cn edge insertions is continuous. A variation of the Erd\"os-R\'enyi process are the so-called Achlioptas processes in which in every step a random pair of edges is drawn, and a fixed edge-selection rule selects one of them to be included in the graph while the other is put back. Recently, Achlioptas, D'Souza and Spencer (2009) gave strong numerical evidence that a variety of edge-selection rules exhibit a discontinuous phase transition. However, Riordan and Warnke (2011) very recently showed that all Achlioptas processes have a continuous phase transition. In this work we prove discontinuous phase transitions for a class of Erd\"os-R\'enyi-like processes in which in every step we connect two vertices, one chosen randomly from all vertices, and one chosen randomly from a restricted set of vertices.
Panagiotou Konstantinos
Spöhel Reto
Steger Angelika
Thomas Henning
No associations
LandOfFree
Explosive Percolation in Erdös-Rényi-Like Random Graph Processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Explosive Percolation in Erdös-Rényi-Like Random Graph Processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Explosive Percolation in Erdös-Rényi-Like Random Graph Processes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-717924