# Spanning trees with few branch vertices

@article{DeBiasio2019SpanningTW, title={Spanning trees with few branch vertices}, author={Louis DeBiasio and Allan Lo}, journal={ArXiv}, year={2019}, volume={abs/1709.04937} }

A branch vertex in a tree is a vertex of degree at least three. We prove that for all positive integers $s$, every connected graph on $n$ vertices with minimum degree at least $(\frac{1}{s+3}+o(1))n$ contains a spanning tree having at most $s$ branch vertices. Asymptotically, this is best possible and solves a problem of Flandrin, Kaiser, Kuuzel, Li and Ryjaucek, which was originally motivated by an optimization problem in the design of optical networks.

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