Opuscula Math. 31, no. 4 (2011), 533-547
http://dx.doi.org/10.7494/OpMath.2011.31.4.533

Opuscula Mathematica

# Recursively arbitrarily vertex-decomposable suns

Olivier Baudon
Frédéric Gilbert
Mariusz Woźniak

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.

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• Olivier Baudon
• LaBRI, Université de Bordeaux, 351, cours de la Libération, 33405 Talence Cedex, France
• Frédéric Gilbert
• LaBRI, Université de Bordeaux, 351, cours de la Libération, 33405 Talence Cedex, France
• Mariusz Woźniak
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
• Revised: 2011-03-26.
• Accepted: 2011-03-28.

Olivier Baudon, Frédéric Gilbert, Mariusz Woźniak, Recursively arbitrarily vertex-decomposable suns, Opuscula Math. 31, no. 4 (2011), 533-547, http://dx.doi.org/10.7494/OpMath.2011.31.4.533

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