Opuscula Math. 31, no. 4 (), 533-547
http://dx.doi.org/10.7494/OpMath.2011.31.4.533
Opuscula Mathematica

# 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.
Mathematics Subject Classification: 05C99, 68R10.