Geodesic
Construction of a spanning tree with many leaves
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part II, Tome 381 (2010), pp. 31-46
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It is well known [4] that any $n$ vertex graph of minimal degree 4 possess a spanning tree with at least $\frac25\cdot n$ vertices, which is asymptotically sharp bound. In current work we present a polynomial algorithm that finds in a graph with $k$ vertices of degree at least four and $k'$ vertices of degree 3 a spanning tree with the number of leaves at least $\lceil\frac25\cdot k+\frac2{15}\cdot k'\rceil$. Bibl. 13 titles. 
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N. V. Gravin. Construction of a spanning tree with many leaves. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part II, Tome 381 (2010), pp. 31-46. http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a1/

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