Leafy spanning k -forests

We denote by Leafy Spanning k - Forest the problem of, given a positive integer k and a graph G with at most k components, finding a spanning forest in G with at most k components and the maximum number of leaves. The case k=1 is known to be NP-hard, and is well studied in the literature, with the best approximation algorithm having been proposed more than 20 years ago by Solis-Oba. The best approximation algorithm known for Leafy Spanning k - Forest is a 3-approximation based on an approach by Lu and Ravi for the k=1 case. We extend the algorithm of Solis-Oba to achieve a 2-approximation for Leafy Spanning k - Forest .