Examples of outerplanar

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We show that every planar graph is (3, 2) -choosable and every outerplanar graph is (2, 2) -choosable.
There are no such o simple formulas known for general outerplanar graphs.
We will then show how to modify the algorithm to generate unlabelled connected outerplanar graphs uniformly at random in expected polynomial time.
In particular, they showed that every outerplanar graph is (2, 2) -colourable and every planar graph is (3, 2) -colourable.
For instance, outerplanar graphs enjoy many nice properties both from an algorithmic and a structural point of view.
This allows us to make the correct probabilistic choices in a recursive generation of uniformly distributed outerplanar graphs.
In this paper we show how to efficiently generate random labelled outerplanar graphs.
In the following sections, when dealing with outerplanar graphs, we will therefore concentrate on the presentation of the decomposition strategy and the counting formulas.
We have found a short direct proof for the (2, 1) -choosability of triangle-free outerplanar graphs.
In this paper, we will focus on the generation of random outerplanar graphs according to their uniform distribution.
Throughout this section we assume that the outerplanar graphs are unlabelled and connected.
The reason why the decomposition into biconnected components of a graph is so useful is that biconnected outerplanar graphs have a simple structure.
We present a uniform generation procedure for outerplanar graphs using rejection sampling.
And all triangle-free outerplanar graphs are (m, d) choosable if and only if (m, d) > (2, 1) or (m, d) > (3, 0).
One may ask whether every planar graph is (3, 1) -choosable and every outerplanar graph is (2, 1) choosable.

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