Transfer matrix for spanning trees, webs and colored forests

Determinantal generating functions of colored spanning forests

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 describe...

Sufficient conditions for the existence of spanning colored trees in edge-colored graphs

Rainbow spanning trees in complete graphs colored by one-factorizations

Brualdi and Hollingsworth conjectured that, for even n, in a proper edge coloring of Kn using precisely n − 1 colors, the edge set can be partitioned into n2 spanning trees which are rainbow (and hence, precisely one edge from each color class is in each spanning tree). They proved that there always are two edge disjoint rainbow spanning trees. Kaneko, Kano and Suzuki improved this to three edg...

Combinatorial optimization with one quadratic term: Spanning trees and forests

The standard linearization of a binary quadratic program yields an equivalent reformulation as an integer linear program, but the resulting LP-bounds are very weak in general. We concentrate on applications where the underlying linear problem is tractable and exploit the fact that, in this case, the optimization problem is still tractable in the presence of a single quadratic term in the object...

NUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS

In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...