Recursively arbitrarily vertex-decomposable graphs

@inproceedings{Baudon2012RecursivelyAV,
  title={Recursively arbitrarily vertex-decomposable graphs},
  author={Olivier Baudon and Fr{\'e}d{\'e}ric Gilbert and Mariusz Wozniak},
  year={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. 

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