Geodesic
A note on $PM$-compact bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 409-413.

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A graph is called perfect matching compact (briefly, PM-compact), if its perfect matching graph is complete. Matching-covered PM-compact bipartite graphs have been characterized. In this paper, we show that any PM-compact bipartite graph G with δ (G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM-compact, which implies that G is matching-covered
Keywords: perfect matching, PM-compact graph, matching-covered graph 
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Liu, Jinfeng; Wang, Xiumei. A note on $PM$-compact bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 409-413. http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a13/

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