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2
votes
Accepted
Approximating max degree $3$ perfect matching count?
polytime deterministic approximation to the number of perfect matchings of a graph of maximum degree 3, and average degree in $[2,3]$ is equal to the best polytime deterministic approximation to the permanent …
6
votes
Accepted
Size of Formulas with no negative sign for Matrix Permanent
Snir has proved a tight lower bound on the size of monotone formulas representing the permanent of an $n\times n$ matrix. … Also, a lower bound of $2^{\Omega(n)}$ on the size of monotone circuits for the permanent is known as well (proved by Jerrum and Snir) …
3
votes
Accepted
What is known about counting bipartite perfect matching with average degree in $[2,3]$ and m...
You can take any degree 3 bipartite graph $G$ and take its disjoint union $G'$ with a cycle $C$ of length 2m. The new graph $G'$ is bipartite, and has average degree $\frac{3n + 2m}{m+n} = 2 + \frac{n …