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Random matching problems on the complete graph

   
@article{ECP1372,
	author = {Johan Wästlund},
	title = {Random matching problems on the complete graph},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Minimum matching, exponential, expectation, mean field, network.},
	abstract = {The edges of the complete graph on $n$ vertices are assigned independent exponentially distributed costs. A $k$-matching is a set of $k$ edges of which no two have a vertex in common. We obtain explicit bounds on the expected value of the minimum total cost $C_{k,n}$ of a $k$-matching. In particular we prove that if $n = 2k$ then $\pi^2/12 < EC_{k,n} < \pi^2/12 + \log n/n$.},
	pages = {no. 25, 258-265},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1372},    
        url = {http://ecp.ejpecp.org/article/view/1372}}