On arbitrarily vertex decomposable trees Original Research Article

A tree image is arbitrarily vertex decomposable if for any sequence image of positive integers adding up to the order of image there is a sequence of vertex-disjoint subtrees of image whose orders are given by image; from a result by Barth and Fournier it follows that image. 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.