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Given a complete weighted graph $G(V,E),\ |V|=2n$, calculating a minimum weight matching with $n-k$ edges can be reduced to calculating a perfect matching in $H(V+U,E+F),\ |U|=2k,\ F=(u\in U,v\in V),\ ...

A fairly wellknown heuristic for TSP that is based on matching is described in the 2003 paper Match twice and stitch: a new TSP tour construction heuristic by Andrew B. Kahng and Sherief Reda. Its ...