| J. Aronson, A.M. Frieze and B. Pittel, Finding matchings in sparse random graphs, in preparation. |
....(a) The algorithm is considered to run in two phases. Phase 1 ends when the minimum degree of the graph that remains is at least two. Note that during Phase 1 the algorithm makes correct choices in the sense that the edges chosen are a subset of some maximum matching. Aronson, Frieze and Pittel [10] have been conducting a further analysis of this algorithm. At this stage it looks as though the following is true whp: ffl If c e then at the end of Phase 1, all that is left of the graph is a few vertex disjoint cycles. ffl If c e then in Phase 2, KSGREEDY will match all but about n 1=5 ....
J. Aronson, A.M. Frieze and B. Pittel, Finding matchings in sparse random graphs, in preparation.
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