d
-regular graph G, let M be chosen uniformly at random from the set of all matchings of G, and for let be the probability that M does not cover x.
We show that for large d, the 's and the mean μ and variance of are determined to within small tolerances just by d and (in the case of μ and ) :
Theorem. For any d-regular graph G,
(a) , so that ,
(b) ,
where the rates of convergence depend only on d.
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Received: April 12, 1996
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Kahn, J., Han Kim, J. Random Matchings in Regular Graphs. Combinatorica 18, 201–226 (1998). https://doi.org/10.1007/PL00009817
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DOI: https://doi.org/10.1007/PL00009817