Geodesic
1-factors and characterization of reducible faces of plane elementary bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 2, pp. 289-297

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As a general case of molecular graphs of benzenoid hydrocarbons, we study plane bipartite graphs with Kekulé structures (1-factors). A bipartite graph G is called elementary if G is connected and every edge belongs to a 1-factor of G. Some properties of the minimal and the maximal 1-factor of a plane elementary graph are given.
Keywords: plane elementary bipartite graph, reducible face, perfect matching, 1-factor, benzenoid graph 
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Taranenko, Andrej; Vesel, Aleksander. 1-factors and characterization of reducible faces of plane elementary bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 2, pp. 289-297. http://geodesic.mathdoc.fr/item/DMGT_2012_32_2_a8/