Recursively Arbitrarily Vertex-Decomposable Graphs ∗
Olivier Baudon, Frédéric Gilbert, Mariusz Woźniak · 2012
A graph G = (V, E) is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to |V |, there is a sequence of vertex-disjoints subsets of V whose orders are given by τ, and which induce connected graphs. The main aim of this paper is to study the recursive version of this problem. We present a solution for trees, suns, and partially for a class of 2-connected graphs called balloons. 1