Kirchhoff’s matrix-tree theorem asserts that the number of spanning trees in a finite graph can be computed from the determinant of any of its reduced Laplacian matrices. In many cases, even for ...

Let G be a finite graph or an infinite graph on which Z d acts with finite fundamental domain. If G is finite, let T be a random spanning tree chosen uniformly from all spanning trees of G; if G is ...

One of the highlights in the Robertson-Seymour theory on graph minors is the finiteness (for each fixed surface S) of the set of the minimal forbidden minors for S. Theorem 7.0.1 (Robertson and ...