Random Matchings in Regular Graphs

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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  • AMS Subject Classification (1991) Classes:  05C65, 05C70, 05C80, 60C05, 60F05, 60G42