All Questions

Suppose we have two bipartite graphs $G_1$ and $G_2$ with perfect matching count $P_1$ and $P_2$ respectively then their disjoint union gives a bipartite graph with perfect matching $P_1P_2$. Is ...

Is there a function which describes the number of $\{0,1\}^{n\times n}\cap\mathbb Z^{n\times n}$ matrices having permanent $1$? I think it might be $\mathsf{poly}(n!)$ bounded. Is there a function ...

What is the maximum number of perfect matchings a genus $g$ balanced $k$-partite graph (number of vertices for each color in all possible $k$-colorings is within a difference of $1$) can have? I am ...

Let $f(G)$ give number of perfect matchings of a graph $G$. Denote $\mathcal N_{2n}=\{0,1,2,\dots,n!-1,n!\}$. Denote collection of all $2n$ vertex balanced bipartite graph to be $\mathcal G_{2n}$. ...

Planar graph permanent can be reduced to determinants and so statistics should be amenable. Pick a uniformly random bipartite planar graph $G$ with $n$ vertices of each color and choose new additional ...