Heterochromatic tree partition numbers for complete bipartite graphs

Abstract: An -edge-coloring of a graph is a surjective assignment of colors to the edges of . A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an -edge-colored graph , denoted by , is the minimum positive integer p such that whenever the edges of the graph are colored with colors, the vertices of 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 -edge-colored complete bipartite graph . [Copyright &y& Elsevier]