A note on the hardness results for the labeled perfect matching problems in bipartite graphs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 3, pp. 315-324.

In this note, we strengthen the inapproximation bound of O(logn) for the labeled perfect matching problem established in J. Monnot, The Labeled perfect matching in bipartite graphs, Information Processing Letters 96 (2005) 81-88, using a self improving operation in some hard instances. It is interesting to note that this self improving operation does not work for all instances. Moreover, based on this approach we deduce that the problem does not admit constant approximation algorithms for connected planar cubic bipartite graphs.

DOI : 10.1051/ro:2008020
Classification : 68Q17, 68R10, 68W25, 90C59
Mots-clés : labeled matching, bipartite graphs, approximation and complexity, inapproximation bounds 
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     author = {Monnot, J\'er\^ome},
     title = {A note on the hardness results for the labeled perfect matching problems in bipartite graphs},
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     pages = {315--324},
     publisher = {EDP-Sciences},
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Monnot, Jérôme. A note on the hardness results for the labeled perfect matching problems in bipartite graphs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 3, pp. 315-324. doi : 10.1051/ro:2008020. https://numdam.org/articles/10.1051/ro:2008020/

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