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].
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