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Accumulation of the phytoalexin glyceollin i in soybean nodules infected by a bradyrhizobium-japonicum-nifa mutant
Even circuits of prescribed clockwise parity
We show that a graph has an orientation under which every circuit of even
length is clockwise odd if and only if the graph contains no subgraph which is,
after the contraction of at most one circuit of odd length, an even subdivision
of K_{2,3}. In fact we give a more general characterisation of graphs that have
an orientation under which every even circuit has a prescribed clockwise
parity. This problem was motivated by the study of Pfaffian graphs, which are
the graphs that have an orientation under which every alternating circuit is
clockwise odd. Their significance is that they are precisely the graphs to
which Kasteleyn's powerful method for enumerating perfect matchings may be
applied
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