A simple approximation algorithm for WIS based on the approximability in k

In this note, we show how optimal or approximate weighted independent sets in k-partite graphs may yield to a good approximate weighted independent set in general graphs. Precisely, optimal solutions in bipartite graphs do yield to a 2 ∆(G) approximation and, more generally, ρ-approximate solutions in k-partite graphs yield to a k ∆(G)ρ-approximation in general graphs.