Complete solution for the rainbow numbers of matchings

Abstract: For a given graph and a positive , the rainbow number of , denoted by , is the minimum integer so that in any edge-coloring of with colors there is a copy of whose edges have distinct colors. In 2004, Schiermeyer determined for all . The case for smaller values of (namely, ) remained generally open. In this paper we extend Schiermeyer’s result to all plausible and hence determine the rainbow number of matchings. [Copyright &y& Elsevier]