Generating Random Outerplanar Graphs
نویسندگان
چکیده
منابع مشابه
Generating Outerplanar Graphs Uniformly at Random
We show how to generate labeled and unlabeled outerplanar graphs with n vertices uniformly at random in polynomial time in n. To generate labeled outerplanar graphs, we present a counting technique using the decomposition of a graph according to its block structure, and compute the exact number of labeled outerplanar graphs. This allows us to make the correct probabilistic choices in a recursiv...
متن کاملVertices of given degree in series-parallel graphs
We show that the number of vertices of a given degree k in several kinds of series-parallel labelled graphs of size n satisfy a central limit theorem with mean and variance proportional to n, and quadratic exponential tail estimates. We further prove a corresponding theorem for the number of nodes of degree two in labelled planar graphs. The proof method is based on generating functions and sin...
متن کاملEvery Property of Outerplanar Graphs is Testable
A D-disc around a vertex v of a graph G = (V,E) is the subgraph induced by all vertices of distance at most D from v. We show that the structure of an outerplanar graph on n vertices is determined, up to modification (insertion or deletion) of at most n edges, by a set of D-discs around the vertices, for D = D( ) that is independent of the size of the graph. Such a result was already known for ...
متن کاملEnumeration of Unlabeled Outerplanar Graphs
We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time, and gn is asymptotically g n −5/2 ρ , where g ≈ 0.00909941 and ρ ≈ 7.50360 can be approximated. Using our enumerative results we investigate several statistical properties of random unlabeled outerplanar graphs on n v...
متن کاملEnumeration and Limit Laws of Series-parallel Graphs
We show that the number gn of labelled series-parallel graphs on n vertices is asymptotically gn ∼ g · n−5/2γnn!, where γ and g are explicit computable constants. We show that the number of edges in random seriesparallel graphs is asymptotically normal with linear mean and variance, and that it is sharply concentrated around its expected value. Similar results are proved for labelled outerplana...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003