A note on the random greedy triangle-packing algorithm

The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. We begin with a complete graph on n vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is chosen uniformly at random from the collection of all remaining triangles. This stochastic process terminates once it arrives at a triangle-free graph. In this note we show that with high probability the number of edges in the final graph is at most O n7/4 log5/4 n .

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Tom Bohman, Alan M. Frieze, Eyal Lubetzky
• Keywords: CORR 2010, Education, Large Partial Steiner-triple-system, Random Greedy Algorithm, Triangles