Vertices of given degree in series-parallel graphs
نویسندگان
چکیده
منابع مشابه
Vertices 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 کاملThe Maximum Degree of Series-Parallel Graphs
MICHAEL DRMOTA, OMER GIMÉNEZ and MARC NOY Combinatorics, Probability and Computing / Volume 20 / Issue 04 / July 2011, pp 529 570 DOI: 10.1017/S0963548311000198, Published online: 31 May 2011 Link to this article: http://journals.cambridge.org/abstract_S0963548311000198 How to cite this article: MICHAEL DRMOTA, OMER GIMÉNEZ and MARC NOY (2011). The Maximum Degree of Series Parallel Graphs. C...
متن کاملDiameter Two Graphs of Minimum Order with Given Degree Set
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
متن کاملThe maximum degree of planar graphs I. Series-parallel graphs
We prove that the maximum degree ∆n of a random series-parallel graph with n vertices satisfies ∆n/ log n → c in probability, and E∆n ∼ c log n for a computable constant c > 0. The same result holds for outerplanar graphs.
متن کاملPoisson convergence of numbers of vertices of a given degree in random graphs
The asymptotic distributions of the number of vertices of a given degree in random graphs, where the probabilities of edges may not be the same, are given. Using the method of Poisson convergence, distributions in a general and particular cases (complete, almost regular and bipartite graphs) are obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2009
ISSN: 1042-9832
DOI: 10.1002/rsa.20290