The diamond-free process
Article first published online: 11 OCT 2013
Copyright © 2013 Wiley Periodicals, Inc.
Random Structures & Algorithms
How to Cite
Picollelli, M. E. (2013), The diamond-free process. Random Struct. Alg.. doi: 10.1002/rsa.20517
- Article first published online: 11 OCT 2013
- Manuscript Accepted: 12 JUN 2013
- Manuscript Revised: 16 MAR 2013
- Manuscript Received: 27 SEP 2010
- H-free process;
- random greedy algorithm;
- differential equations method
Let denote the diamond graph, formed by removing an edge from the complete graph K4. We consider the following random graph process: starting with n isolated vertices, add edges uniformly at random provided no such edge creates a copy of . We show that, with probability tending to 1 as , the final size of the graph produced is . Our analysis also suggests that the graph produced after i edges are added resembles the uniform random graph, with the additional condition that the edges which do not lie on triangles form a random-looking subgraph. © 2013 Wiley Periodicals, Inc.