Geodesic
An attractive class of bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 2, pp. 293-301

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In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.
Keywords: bipartite graphs, structural characterization, polynomial algorithm 
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Boliac, Rodica; Lozin, Vadim. An attractive class of bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 2, pp. 293-301. http://geodesic.mathdoc.fr/item/DMGT_2001_21_2_a12/