Spanning trees with many leaves

Let maximal chain of vertices of degree 2 in the graph $G$ consists of $k>0$ vertices. We prove that $G$ has a spanning tree with more than $\frac{v(G)}{2k+4}$ leaves (we denote by $v(G)$ the number of vertices of the graph $G$). We present an infinite serie of examples showing that the constant $\frac1{2k+4}$ cannot be enlarged. Bibl. 7 titles.