Determinantal generating functions of colored spanning forests

Abstract

The color type of a spanning forest of a graph with colored edges is defined and, subsequently, it is proved that the generating function of such spanning forests is obtained as the formal expansion of a certain determinant. An analogous determinantal expansion yields the generating function of all spanning forests of a given color type that contain a specific subforest. Algorithms are described for obtaining a list of all colored spanning trees and spanning forests of any graph with colored edges based on symbolic calculation.