Geodesic
Spanning trees with many or few colors in edge-colored graphs
Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 259-269.

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Given a graph G = (V,E) and a (not necessarily proper) edge-coloring of G, we consider the complexity of finding a spanning tree of G with as many different colors as possible, and of finding one with as few different colors as possible. We show that the first problem is equivalent to finding a common independent set of maximum cardinality in two matroids, implying that there is a polynomial algorithm. We use the minimum dominating set problem to show that the second problem is NP-hard.
Keywords: edge-coloring, spanning tree, matroid (intersection), complexity, NP-complete, NP-hard, polynomial algorithm, (minimum) dominating set 
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Broersma, Hajo; Li, Xueliang. Spanning trees with many or few colors in edge-colored graphs. Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 259-269. http://geodesic.mathdoc.fr/item/DMGT_1997_17_2_a4/

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