Geodesic
Spanning trees with many leaves
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part II, Tome 381 (2010), pp. 78-87

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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. 
@article{ZNSL_2010_381_a3,
     author = {D. V. Karpov},
     title = {Spanning trees with many leaves},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {78--87},
     publisher = {mathdoc},
     volume = {381},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a3/}
}
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D. V. Karpov. Spanning trees with many leaves. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part II, Tome 381 (2010), pp. 78-87. http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a3/