Open Access
2008 Random matching problems on the complete graph
Johan Wästlund
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Electron. Commun. Probab. 13: 258-265 (2008). DOI: 10.1214/ECP.v13-1372


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 $\pi^2/12 < EC_{k,n} < \pi^2/12 + \log n/n$.


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Johan Wästlund. "Random matching problems on the complete graph." Electron. Commun. Probab. 13 258 - 265, 2008.


Accepted: 12 May 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60027
MathSciNet: MR2415133
Digital Object Identifier: 10.1214/ECP.v13-1372

Primary: 60C05
Secondary: 90C27 , 90C35

Keywords: expectation , exponential , Mean field , Minimum matching , network

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