Maximum matching in sparse random graphs

@article{Karp1981MaximumMI,
  title={Maximum matching in sparse random graphs},
  author={Richard M. Karp and Michael Sipser},
  journal={22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)},
  year={1981},
  pages={364-375}
}
We study the average performance of a simple greedy algorithm for nding a matching in a sparse random graph G n;c=n , where c > 0 is constant. The algorithm was rst proposed by Karp and Sipser 12]. We give signiicantly improved estimates of the errors made by the algorithm. For the sub-critical case where c < e we show that the algorithm nds a maximum matching with high probability. If c > e then with high probability the algorithm produces a matching which is within n 1=5+o(1) of maximum size. 
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