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Abstract: A tree $T$ is arbitrarily vertex decomposable if for any sequence $\tau$ of positive integers adding up to the order of $T$ there is a sequence of vertex-disjoint subtrees of $T$ whose orders are given by $\tau$; from a result by Barth and Fournier it follows that $\Delta(T)\le4$. 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. Contact the authors: mirko.hornak@upjs.sk, mwozniak@uci.agh.edu.pl Download PDF version of the preprint. |