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A subgraph of a graph is if has a
perfect matching. An orientation of is if, for
every conformal even circuit , the number of edges of whose
directions in agree with any prescribed sense of orientation of
is odd. A graph is if it has a Pfaffian
orientation. Not every graph is Pfaffian. However, if has a
Pfaffian orientation , then the determinant of the adjacency matrix
of is the square of the number of perfect matchings of . (See
the book by Lovász and Plummer [.
Annals of Discrete...
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