Geodesic
Spanning trees with many leaves: lower bounds in terms of number of vertices of degree~1, 3 and at least~4
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part V, Tome 406 (2012), pp. 67-94

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We prove that every connected graph with $s$ vertices of degree 1 and 3 and $t$ vertices of degree at least 4 has a spanning tree with at least $\frac13t+\frac14s+\frac32$ leaves. We present an infinite series of graphs showing that our bound is tight. 
@article{ZNSL_2012_406_a3,
     author = {D. V. Karpov},
     title = {Spanning trees with many leaves:  lower bounds in terms of number of vertices of degree~1, 3 and at least~4},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--94},
     publisher = {mathdoc},
     volume = {406},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_406_a3/}
}
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D. V. Karpov. Spanning trees with many leaves:  lower bounds in terms of number of vertices of degree~1, 3 and at least~4. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part V, Tome 406 (2012), pp. 67-94. http://geodesic.mathdoc.fr/item/ZNSL_2012_406_a3/