Name
Abstract | ||
|---|---|---|
The study of the phase transition of random graph processes, and recently in particular Achlioptas processes, has attracted much attention. Achlioptas, D'Souza and Spencer Science, 2009 gave strong numerical evidence that a variety of edge-selection rules in Achlioptas processes exhibit a discontinuous phase transition. However, Riordan and Warnke Science, 2011 recently showed that all these processes have a continuous phase transition. In this work we prove discontinuous phase transitions for three random graph processes: all three start with the empty graph on n vertices and, depending on the process, we connect in every step i one vertex chosen randomly from all vertices and one chosen randomly from a restricted set of vertices, ii two components chosen randomly from the set of all components, or iii a randomly chosen vertex and a randomly chosen component. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1017/S0963548312000442 | Electronic Notes in Discrete Mathematics |
Keywords | DocType | Volume |
n vertex,explosive percolation,continuous phase transition,phase transition,discontinuous phase transition,spencer science,random graph process,nyi-like random graph process,warnke science,particular achlioptas process,empty graph,achlioptas process | Journal | 22 |
Issue | ISSN | Citations |
1 | 0963-5483 | 1 |
PageRank | References | Authors |
0.39 | 2 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Konstantinos Panagiotou | 1 | 290 | 27.80 |
| Reto Spöhel | 2 | 94 | 11.11 |
| Angelika Steger | 3 | 995 | 111.50 |
| Henning Thomas | 4 | 35 | 3.96 |