Opuscula Math. 32, no. 4 (2012), 689-706
http://dx.doi.org/10.7494/OpMath.2012.32.4.689
Opuscula Mathematica
Recursively arbitrarily vertex-decomposable graphs
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 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: arbitrary vertex decomposable (AVD) graph, recursively AVD graphs.
Mathematics Subject Classification: 05C99, 68R10.
- Olivier Baudon
- Univ. Bordeaux, LaBRI, UMR 5800, F-33400 Talence, France
- CNRS, LaBRI, UMR 5800, F-33400 Talence, France
- Frédéric Gilbert
- Univ. Bordeaux, LaBRI, UMR 5800, F-33400 Talence, France
- CNRS, LaBRI, UMR 5800, F-33400 Talence, France
- Mariusz Woźniak
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
- Received: 2011-07-02.
- Revised: 2012-02-08.
- Accepted: 2012-02-09.
