Approximation algorithms for the minimum rainbow subgraph problem

We consider the minimum rainbow subgraph problem (MRS): given a graph G, whose edges are coloured with p colours. Find a subgraph F⊆G of G of minimum order and with p edges such that each colour occurs exactly once. For graphs with maximum degree Δ(G) there is a greedy polynomial-time approximation algorithm for the MRS problem with an approximation ratio of Δ(G). In this paper we present a polynomial-time approximation algorithm with an approximation ratio of View the MathML source for Δ≥2.