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arXiv · 1205.5163

Spanning trees with many leaves: lower bounds in terms of number of vertices of degree 1, 3 and at least~4

Dmitri Karpov
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Abstract

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 ${1\over 3}t +{1\over 4}s+{3\over 2}$ leaves. We present infinite series of graphs showing that our bound is tight.

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Dmitri Karpov. 2012-05-23. Spanning trees with many leaves: lower bounds in terms of number of vertices of degree 1, 3 and at least~4. https://doi.org/10.1007/s10958-014-1692-7

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