On the number of cycles in a random non-equiprobable graph

Abstract

We consider a non-

Asymptotics for dependent sums of random vectors

“…The first linear dependence of a random sequence has been studied by several authors, including Balakin, Kolchin, and Khokhlov [3,4], Calkin [5,6], Kolchin [10], and Kolchin and Khokhlov [11]. For 2 and k = 2 the solution m ≤ n/2 is well known.…”

Random graphs and systems of linear equations in finite fields

“…Therefore S(A) is equal to the number of independent cycles in Gn,T. Thus, the results about the distribution of the number of cycles on random graphs[3,8,10,12] can be reformulated on the language of ranks of the corresponding matrices. These considerations lead us to a new concept of cycles in hypergraphs.…”

Consistency of a system of random congruences

“…If n, T -> oo in such a way that 2T/n -> λ, Ο < λ < 1, then This result gives a possibility to prove that the distribution of the number of cycles of various types of random graphs converges to the Poisson distribution. In [5] this possibility is realized for the graph G n> r considered in the present paper.…”

“…[2][3][4][5][6][7]). If π, Τ -> oo in such a way that 2T/n -> λ, Ο < λ < 1, then, with probability tending to one, the graph (7 η ,τ contains no connected components including more than one cycle, therefore, with probability tending to one, cycles in the graph Ο η ,τ are independent and ί/η,τ = θ(ν4 η , τ ).…”