Recursively arbitrarily vertex-decomposable graphs

Olivier Baudon (1) , Frédéric Gilbert (1, 2) , Mariusz Woźniak (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 GRAVITE - Graph Visualization and Interactive Exploration
3 AGH UST - AGH University of Science and Technology [Krakow, PL]

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.

Keywords: Vertex-decomposable graphs

Domains: Discrete Mathematics [cs.DM]

Olivier Baudon, Frédéric Gilbert, Mariusz Woźniak. Recursively arbitrarily vertex-decomposable graphs. 2012. ⟨hal-00738153⟩