Complete solution for the rainbow numbers of matchings

For a given graph H and a positive n , the rainbow number of H , denoted by r b ( n , H ) , is the minimum integer k so that in any edge-coloring of K n with k colors there is a copy of H whose edges have distinct colors. In 2004, Schiermeyer determined r b ( n , k K 2 ) for all n ≥ 3 k + 3 . The case for smaller values of n (namely, n ∈ [ 2 k , 3 k + 2 ] ) remained generally open. In this paper we extend Schiermeyer’s result to all plausible n and hence determine the rainbow number of matchings.