On plane bipartite graphs without fixed edges

-An edge of a graph H with a perfect matching is a fixed edge if it either belongs to none or to all of the perfect matchings of H. It is shown that a connected plane bipartite graph has no fixed edges if and only if the boundary of every face is an alternating cycle. Moreover, a polyhex fragment has no fixed edges if and only if the boundaries of its infinite face and the non-hexagonal finite faces are alternating cycles. These results extend results on generalized hexagonal systems from [1]. Keywords---Perfect matching, Fixed edge, Alternating cycle, Plane bipartite graph, Polyhex fragment, Generalized hexagonal system. AMS subject classification (2000): 92E10, 05C70

• Type: Journal
• Year: 2007
• Where: APPML
• Authors: Khaled Salem, Sandi Klavzar
• Keywords: APPML 2007, Fixed Edge, Perfect Matchings, Plane Bipartite Graph