Isolated cycles of critical random graphs
نویسندگان
چکیده
Consider the Erdős-Rényi random graph G(n, M) built with n vertices and M edges uniformly randomly chosen from the set of ( n 2 ) edges. Let L be a set of positive integers. For any number of edges M 6 n/2 + O(n), we compute – via analytic combinatorics – the number of isolated cycles of G(n, M) whose length is in L.
منابع مشابه
On the Structure of the Core of Sparse Random Graphs
In this paper, we investigate the structure of the core of a sparse random graph above the critical point. We determine the asymptotic distributions of the total number of isolated cycles there as well as the joint distributions of the isolated cycles of fixed lengths. Furthermore, focusing on its giant component, we determine the asymptotic joint distributions of the cycles of fixed lengths th...
متن کامل0n removable cycles in graphs and digraphs
In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...
متن کاملVertex Removable Cycles of Graphs and Digraphs
In this paper we defined the vertex removable cycle in respect of the following, if $F$ is a class of graphs(digraphs) satisfying certain property, $G in F $, the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $. The vertex removable cycles of eulerian graphs are studied. We also characterize the edge removable cycles of regular graphs(digraphs).
متن کاملIntersecting random graphs and networks with multiple adjacency constraints: A simple example
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations. A simple idea to account for multiple constraints consists in taking the intersection of random graphs. In this paper we initiate the study of random graphs ...
متن کاملJa n 20 09 Bounds for the return probability of the delayed random walk on finite percolation clusters in the critical case
By an eigenvalue comparison-technique[20], the expected return probability of the delayed random walk on critical Bernoulli bond percolation clusters on the twodimensional Euclidean lattice is estimated. The results are generalised to invariant percolations on unimodular graphs with almost surely finite clusters. The approach involves using the special property of cartesian products of finite g...
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 2017