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I need to count the number of perfect matchings of a certain family of graphs. This family of graph is non planar and a type of snark. For the initial cases, it seems that this number is growing ...

In the definition of this problem, the weight/cost function generally takes value in $\mathbb{Z}$ (or sometimes $\mathbb{Q}$). This is what I observed from some books (e.g. "Combinatorial ...