The distribution of the number of small cuts in a random planar triangulation
نویسندگان
چکیده
We enumerate rooted 3-connected (2-connected) planar triangulations with respect to the vertices and 3-cuts (2-cuts). Consequently, we show that the distribution of the number of 3-cuts in a random rooted 3-connected planar triangulation with n+3 vertices is asymptotically normal with mean (10/27)n and variance (320/729)n, and the distribution of the number of 2-cuts in a random 2-connected planar triangulation with n + 2 vertices is asymptotically normal with mean (8/27)n and variance (152/729)n. We also show that the distribution of the number of 3-connected components in a random 2-connected triangulation with n+ 2 vertices is asymptotically normal with mean n/3 and variance 8 27 n.
منابع مشابه
Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach
The hub location problem arises in a variety of domains such as transportation and telecommunication systems. In many real-world situations, hub facilities are subject to disruption. This paper deals with the multiple allocation hub location problem in the presence of facilities failure. To model the problem, a two-stage stochastic formulation is developed. In the proposed model, the number of ...
متن کاملDetermination of Optimum Planar Imaging Parameters for Small Structures with Diameters Less Than the Resolution of the Gamma Camera
Introduction: The limited spatial resolution of the gamma camera hinders the absolute quantification of planar images of small structures. The imaged structures are affected by partial volume effects (PVEs), which can spread activity and lead to underestimation of the regional distribution. The use of optimum planar parameters reduces the impact of the limited spatial resolution of the gamma c...
متن کاملSharp Concentration of the Number of Submaps in Random Planar Triangulations
We show that the maximum vertex degree in a random 3-connected planar triangulation is concentrated in an interval of almost constant width. This is a slightly weaker type of result than our earlier determination of the limiting distribution of the maximum vertex degree in random planar maps and in random triangulations of a (convex) polygon. We also derive sharp concentration results on the nu...
متن کاملThe Study of Triangulation Forms and Their Relationship with Parenting Styles among Families in Yazd
Introduction: The family provides the first seed of human development and personality development. The child learns ethical principles and social relationships with others in the family. So it is important to know what relationships are in the parents’ family and how they raise their children. The main purpose of this study was to investigate triangulation forms and their relationship with pare...
متن کاملDesigning and Fabrication of a New Radiofrequency Planar microcoil for mini-Nuclear Magnetic Resonance
Introduction Radiofrequency planar microcoils are used to increase the resolution of magnetic resonance images of small samples. In this study, we aimed to design and fabricate a spiral planar microcoil constructed on a double-sided printed circuit board (PCB). It has four rings with an internal diameter of 241 microns tuned and matched at 63.8 MHz. Materials and Methods To achieve the maximum ...
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 2010