Poisson Approximation of the Number of Cliques in Random Intersection Graphs
نویسندگان
چکیده
منابع مشابه
Poisson Approximation of the Number of Cliques in Random Intersection Graphs
A random intersection graph G(n,m, p) is defined on a set V of n vertices. There is an auxiliary set W consisting of m objects, and each vertex v ∈ V is assigned a random subset of objects Wv ⊆ W such that w ∈ Wv with probability p, independently for all v ∈ V and all w ∈ W . Given two vertices v1, v2 ∈ V, we set v1 ∼ v2 if and only if Wv1 ∩Wv2 = ∅. We use Stein’s method to obtain an upper boun...
متن کاملMaximum Cliques in Graphs with Small Intersection Number and Random Intersection Graphs
In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for graphs with small intersection number and random intersection graphs (a model in which each one of m labels is chosen independently with probability p by each ...
متن کاملLarge Cliques in Sparse Random Intersection Graphs
Given positive integers n and m, and a probability measure P on {0, 1, . . . ,m}, the random intersection graph G(n,m,P ) on vertex set V = {1, 2, . . . , n} and with attribute set W = {w1, w2, . . . , wm} is defined as follows. Let S1, S2, . . . , Sn be independent random subsets of W such that for any v ∈ V and any S ⊆ W we have P(Sv = S) = P (|S|)/ ( m |S| ) . The edge set of G(n,m,P ) consi...
متن کاملSome lower bounds for the $L$-intersection number of graphs
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
متن کاملRandom Subcube Intersection Graphs I: Cliques and Covering
We study random subcube intersection graphs, that is, graphs obtained by selecting a random collection of subcubes of a fixed hypercube Qd to serve as the vertices of the graph, and setting an edge between a pair of subcubes if their intersection is non-empty. Our motivation for considering such graphs is to model ‘random compatibility’ between vertices in a large network. For both of the model...
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: Journal of Applied Probability
سال: 2010
ISSN: 0021-9002,1475-6072
DOI: 10.1239/jap/1285335412