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The tree partition number of an r-edge-colored graph G, denoted by t r (G), is the minimum number k such that whenever the edges of G are colored with r colors, the vertices of G can be covered by at most k vertex-disjoint monochromatic trees. We determine t 2 (K(n 1 , n 2 ,. .. , n k)) of the complete k-partite graph K(n 1 , n 2 ,. .. , n k). In(More)