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Structural Properties of Recursively Partitionable Graphs with Connectivity 2

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Baudon O., Bensmail J., Foucaud F., Pilśniak M.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 1

89-115

A connected graph G is said to be arbitrarily partitionable (AP for short) if for every partition (n1, . . . , np) of |V (G)| there exists a partition (V1, . . . , Vp) of V (G) such that each Vi induces a connected subgraph of G on ni vertices. Some stronger versions of this property were introduced, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition of G must not only be connected but also fulfil additional conditions. In this paper, we point out some structural properties of OL-AP and R-AP graphs with connectivity 2. In particular, we show that deleting a cut pair of these graphs results in a graph with a bounded number of components, some of whom have a small number of vertices. We obtain these results by studying a simple class of 2-connected graphs called balloons.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Baudon O.

1 Bensmail J.

1 Foucaud F.

1 Pilśniak M.

1 2017

Wyniki wyszukiwania

Structural Properties of Recursively Partitionable Graphs with Connectivity 2