Let *G* be a connected graph on *n* ≥ 2 vertices with girth at least *g* such that the length of a maximal chain of successively adjacent vertices of degree 2 in *G* does not exceed *k* ≥ 1. Denote by *u*(*G*) the maximum number of leaves in a spanning tree of *G*. We prove that *u*(*G*) ≥ *α*_{
g,k
}(*υ*(*G*) *− k −* 2) + 2 where \( {\alpha}_{g,1}=\frac{\left[\frac{g+1}{2}\right]}{4\left[\frac{g+1}{2}\right]+1} \) and \( {\alpha}_{g,k}=\frac{1}{2k+2} \) for *k* ≥ 2. We present an infinite series of examples showing that all these bounds are tight.

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Translated from *Zapiski Nauchnykh Seminarov POMI*, Vol. 450, 2016, pp. 62–73.

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Karpov, D.V. Lower Bounds on the Number of Leaves in Spanning Trees.
*J Math Sci* **232, **36–43 (2018). https://doi.org/10.1007/s10958-018-3857-2

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