Spanning k-ended trees of 3-regular connected graphs

A tree is called k-ended tree if it has at most k leaves, where a leaf is a vertex of degree one. In this paper we prove that every 3-regular connected graph with n vertices such that n is greater than 7 has spanning sub tree with at most [(n+2)/5]-ended tree. At the end we give a conjecture about spanning k-ended trees on 3-regular connected graphs.