Geodesic
Pₘ-saturated bipartite graphs with minimum size
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 197-211

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A graph G is said to be H-saturated if G is H-free i.e., (G has no subgraph isomorphic to H) and adding any new edge to G creates a copy of H in G. In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n;Pₘ) of Pₘ-saturated graph of order n. They gave the number sat(n;Pₘ) for n big enough. We deal with similar problem for bipartite graphs.
Keywords: graph, saturated graph, extremal graph, bipartite graph 
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Dudek, Aneta; Wojda, A. Pₘ-saturated bipartite graphs with minimum size. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 197-211. http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a3/