  Graphical condensation is a technique used to prove combinatorial identities
among numbers of perfect matchings of plane graphs. Propp and Kuo first applied
this technique to prove identities for bipartite graphs. Yan, Yeh, and Zhang
later applied graphical condensation to nonbipartite graphs to prove more
complex identities. Here we generalize some of the identities of Yan, Yeh, and
Zhang. We also describe the latest generalization of graphical condensation in
which the number of perfect matchings of a plane graph is expressed as a
Pfaffian or a determinant where the entries are also numbers of perfect
matchings of subgraphs.
