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In 2001, Brualdi and Hollingsworth proved that an edge-colored balancedcomplete bipartite graph Kn,n with a color set C = {1,2,3,..., 2n-1} has aheterochromatic spanning tree if the number of edges colored with colors in Ris more than |R|^2 /4 for any non-empty subset R \subseteq C, where aheterochromatic spanning tree is a spanning tree whose edges have distinctcolors, namely, any color appears at most once. In 2010, Suzuki generalizedheterochromatic graphs to f-chromatic graphs, where any color c appears at mostf(c). Moreover, he presented a necessary and sufficient condition for graphs tohave an f-chromatic spanning forest with exactly w components. In this paper,using this necessary and sufficient condition, we generalize theBrualdi-Hollingsworth theorem above.

An f-chromatic spanning forest of edge-colored complete bipartite graphs