Recursively arbitrarily vertex-decomposable suns

Abstract

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. Woźniak, Recursively arbitrarily vertex-decomposable graphs, research report, 2010].

Keywords

• arbitrarily vertex-decomposable graphs (AVD)
• recursively AVD graphs