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 5 6 Δ for Δ ≥ 2 .