Abstract: We consider the minimum rainbow subgraph problem (MRS): given a graph , whose edges are coloured with colours. Find a subgraph of of minimum order and with edges such that each colour occurs exactly once. For graphs with maximum degree there is a greedy polynomial-time approximation algorithm for the MRS problem with an approximation ratio of . In this paper we present a polynomial-time approximation algorithm with an approximation ratio of for . [ABSTRACT FROM AUTHOR]