Avoiding small subgraphs in Achlioptas processes

  title={Avoiding small subgraphs in Achlioptas processes},
  author={Michael Krivelevich and Po-Shen Loh and Benny Sudakov},
  journal={Random Struct. Algorithms},
For a fixed integer r, consider the following random process. At each round, one is presented with r random edges from the edge set of the complete graph on n vertices, and is asked to choose one of them. The selected edges are collected into a graph, which thus grows at the rate of one edge per round. This is a natural generalization of what is known in the literature as an Achlioptas process (the original version has r = 2), which has been studied by many researchers, mainly in the context of… CONTINUE READING
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