Bounds of the number of leaves of spanning trees
2012
We prove that every connected graph with $s$ vertices of degree not 2 has a spanning tree with at least ${1\over 4}(s-2)+2$ leaves.
Let $G$ be a be a connected graph of girth $g$ with $v>1$ vertices. Let maximal chain of successively adjacent vertices of degree 2 in the graph $G$ does not exceed $k\ge 1$. We prove that $G$ has a spanning tree with at least $\alpha_{g,k}(v(G)-k-2)+2$ leaves, where $\alpha_{g,k}= {[{g+1\over2}]\over [{g+1\over2}](k+3)+1}$ for $k
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