Abstract:We investigate the ratio I(G) of the average size of a maximal matching to the size of a maximum matching in a graph G. If many maximal matchings have a size close to ν(G), this graph invariant has a value close to 1. Conversely, if many maximal matchings have a small size, I(G) approaches 1 2 . We propose a general technique to determine the asymptotic behavior of I(G) for various classes of graphs. To illustrate the use of this technique, we first show how it makes it possible to find known asymptotic values… Show more
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