20
votes
5answers
1k views

About properties of adjacency matrix when a graph is planar

1- Is there any specific properties for adjacency matrix when a graph is planar? 2- Is there any thing special for computing the permanent of adjacency matrix when a graph is planar?
21
votes
2answers
661 views

Is there a direct/natural reduction to count non-bipartite perfect matchings using the permanent?

Counting the number of perfect matchings in a bipartite graph is immediately reducible to computing the permanent. Since finding a perfect matching in a non-bipartite graph is in NP, there exists ...