On-line arbitrarily vertex decomposable trees
A tree T  is arbitrarily vertex decomposable if for any sequence ? ? 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 ? ? . An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.
on-line arbitrarily vertex decomposable graphs