Efficiently Coloring the Intersection of a General Matroid and Combinatorial Matroids

This paper shows a polynomial-time algorithm that, given a general matroid $M_1$ and $k-1$ partition matroids $ M_2, \ldots, M_k$, produces a coloring of the intersection $M = \cap_{i=1}^k M_i$ using at most $1+\sum_{i=1}^k \left(χ(M_i) -1\right)$ colors. This is the first polynomial-time $O(k)$-app