Consider a matroid or rank n in which each element has a real-valued cost and one of d>1 colors. A class of matroid intersection problems is studied in which one of the matroids is a partition matroid that specifies that a base has qj elements of color j, for j=1,2,...,d. Relationships are characterized among the solutions to the family of problems generated when the vector (q1,q2,...,qd) is allowed to range over all values that sum to n. A fast algorithm is given for solving such matroid intersection problems when d is small. A characterization is presented for how the solution changes when one element changes in cost. Data structures are given for updating the solution on-line each time the cost of an arbitrary matroid element is modified. Efficient update algorithms are given for maintaining a color-constrained minimum spanning tree in either a general or a planar graph. An application of the techniques to the problem of finding a minimum spanning tree with several degree-constrained vertices is described.
