The Labeled perfect matching in bipartite graphs
Résumé
In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph $G=(V,E)$ with $|V|=2n$ vertices such that $E$ contains a perfect matching (of size $n$), together with a color (or label) function $L:E\rightarrow \{c_1,\ldots,c_q\}$, the labeled perfect matching problem consists in finding a perfect matching on $G$ that uses a minimum or a maximum number of colors.
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