# Weighted Counting of Matchings in Unbounded-Treewidth Graph Families

@article{Amarilli2022WeightedCO, title={Weighted Counting of Matchings in Unbounded-Treewidth Graph Families}, author={Antoine Amarilli and Mika{\"e}l Monet}, journal={ArXiv}, year={2022}, volume={abs/2205.00851} }

We consider a weighted counting problem on matchings, denoted PrMatching p G q , on an arbitrary fixed graph family G . The input consists of a graph G P G and of rational probabilities of existence on every edge of G , assuming independence. The output is the probability of obtaining a matching of G in the resulting distribution, i.e., a set of edges that are pairwise disjoint. It is known that, if G has bounded treewidth , then PrMatching p G q can be solved in polynomial time. In this paper…

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