On arbitrarily vertex decomposable trees

@article{Hornk2008OnAV,
  title={On arbitrarily vertex decomposable trees},
  author={Mirko Horn{\'a}k and Mariusz Wozniak},
  journal={Discrete Mathematics},
  year={2008},
  volume={308},
  pages={1268-1281}
}
A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertexdisjoint subtrees of T whose orders are given by τ ; from a result by Barth and Fournier it follows that ∆(T ) ≤ 4. A necessary and a sufficient condition for being an arbitrarily vertex decomposable star-like tree have been exhibited. The conditions seem to be very close to each other. 

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