Max-leaves spanning tree is APX-hard for cubic graphs

We consider the problem of finding a spanning tree with maximum number of leaves. A 2-approximation algorithm is known for this problem, and a 3/2-approximation algorithm when restricted to graphs where every vertex has degree 3 (cubic graphs). The problem is known to be APX-hard in general, and NP-hard for cubic graphs. We show that it is also APX-hard for cubic graphs. The APX-hardness of the related problem Minimum Connected Dominating Set for cubic graphs follows.