Heterochromatic tree partition numbers for complete bipartite graphs Original Research Article

An image-edge-coloring of a graph image is a surjective assignment of image colors to the edges of image. A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an image-edge-colored graph image, denoted by image, is the minimum positive integer p such that whenever the edges of the graph image are colored with image colors, the vertices of image can be covered by at most p vertex-disjoint heterochromatic trees. In this paper we give an explicit formula for the heterochromatic tree partition number of an image-edge-colored complete bipartite graph image.