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Aug 1, 2010 at 19:20 comment added Tsuyoshi Ito I do not expect that your method leads to a polynomial-time algorithm, because it seems that it would equally work in the case where G is not necessarily bipartite, where the problem is known to be #P-complete according to the references in the question.
Feb 4, 2010 at 9:13 history answered Gerhard Paseman CC BY-SA 2.5