Since each page admits an outerplanar graph, G can be decomposed into p outerplanar graphs.
If G = (V,E) is an outerplanar graph, then |E|[less than or equal to]2|V|-3.
6]] Let G = (V,E) be an outerplanar graph with |V| = N.
The pagenumber of a graph G is at least as large as the minimum number of outerplanar graphs into which G can be decomposed.
k] be the limit probability that a vertex of a connected outerplanar graph has degree k then
After some preliminaries, we obtain the degree distribution in simpler families of planar graphs: outerplanar graphs (Section 3) and series-parallel graphs (Section 4).
From the equivalence between rooted 2-connected outerplanar graphs and polygon dissections where the vertices are labelled 1, 2, .
The radius of convergence of C(x) is, as for outerplanar graphs, [rho] = [psi]([tau]), where [psi](u) = u[e.
n,m] be a graph drawn uniformly at random from the set of all labeled connected outerplanar graphs
with n vertices and m edges, where m = [cn] and c [member of] (1,2).
It has recently led to immense progress in the enumeration and the understanding of several properties (such as the distribution of the number of edges and the number of (bi-)connected components) of constrained graph classes, as for instance planar, series parallel, and outerplanar graphs [GN05, BGKN05].
Here we exploit generating function techniques, which were only recently applied to obtain similar results for planar, series parallel, and outerplanar graphs [BGKN05, GN05], and are well described in the forthcoming book "Analytic Combinatorics" by Flajolet and Sedgewick [FS05].
On the number of series parallel and outerplanar graphs.