Recursively arbitrarily vertex-decomposable suns

A graph G = (V;E) is arbitrarily vertex decomposable if for any sequence $\tau$ of positive integers adding up to |V|, there is a sequence of vertex-disjoint subsets of V whose orders are given by $\tau$ , and which induce connected graphs. The aim of this paper is to study the recursive version of this problem on a special class of graphs called suns. This paper is a complement of [O. Baudon, F. Gilbert, M. Wo niak, Recursively arbitrarily vertex-decomposable graphs, research report, 2010].