A note on the random greedy triangle-packing algorithm

Abstract

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 log n )

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Cite this paper

@article{Bohman2010ANO, title={A note on the random greedy triangle-packing algorithm}, author={Tom Bohman and Alan M. Frieze and Eyal Lubetzky}, journal={CoRR}, year={2010}, volume={abs/1004.2418} }