Maximum matchings in sparse random graphs: Karp-Sipser revisited

Abstract

We study the average performance of a simple greedy algorithm for finding a matching in a sparse random graph Gn, c/n, where c>0 is constant. The algorithm was first proposed by Karp and Sipser [Proceedings of the Twenty-Second Annual IEEE Symposium on Foundations of Computing, 1981, pp. 364–375]. We give significantly improved estimates of the errors made by the algorithm. For the subcritical case where c e then with high probability the algorithm produces a matching which is within n1/5+o(1) of maximum size. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 111–177, 1998