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Recursively arbitrarily vertex-decomposable graphs

Baudon O., Gilbert F., Woźniak M.

Opuscula Mathematica

2012

Vol. 32, no. 4

689-706

A graph G = (V, E) is arbitrarily vertex decomposable if for any sequence ϒ of positive integers adding up to/V/, there is a sequence of vertex-disjoint subsets of V whose orders are given by ϒ, 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.

Recursively arbitrarily vertex-decomposable suns

Baudon O., Gilbert F., Woźniak M.

Opuscula Mathematica

2011

Vol. 31, no. 4

533-547

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-disjoint subsets of V whose orders are given by τ , 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].