A short note on the approximability of the maximum leaves spanning tree problem

We prove that the NP-hard problem of finding in an undirected graph G a spanning tree with a maximum number of leaves is MAX-SNP hard. On the basis of a recent result in the theory of approximability of NP-hard optimization problems stating that all problems that are MAX-SNP hard with respect to approximation-preserving reductions do not allow polynomial time approximation schemes, unless P = NP, we conclude that the Maximum Leaves Spanning Tree Problem does not have a polynomial time approximation scheme, unless P = NP, giving therefore a negative answer to this question, which was left open in previous works.