Related papers: On the very weak 0-1 law for random graphs with or…

We find a logic really stronger than first order for the random graph with edge probability $\frac 12$ but satisfies the 0-1 law. This means that on the one hand it satisfies the 0-1 law, e.g. for the random graph ${\mathcal G}_{n,1/2}$ and…

Let G_<(n,p) denote the usual random graph G(n,p) on a totally ordered set of n vertices. We will fix p=1/2 for definiteness. Let L^< denote the first order language with predicates equality (x=y), adjacency (x~y) and less than (x<y). For…

Shelah Spencer [ShSp:304] proved the 0-1 law for the random graphs G(n,p_n), p_n=n^{- alpha}, alpha in (0,1) irrational (set of nodes in [n]= {1, ...,n}, the edges are drawn independently, probability of edge is p_n). One may wonder what…

Let G_n be the random graph on [n]= {1, ...,n} with the possible edge {i,j} having probability being p_{|i-j|}= 1/|i-j|^alpha, alpha in (0,1) irrational. We prove that the zero one law (for first order logic) holds. The paper is continued…

Let $\alpha\in(0,1)_\mathbb{R}$ be irrational and $G_n = G_{{n, 1/n}^\alpha}$ be the random graph with edge probability $1/n^\alpha$; we know that it satisfies the 0-1 law for first order logic. We deal with the failure of the 0-1 law for…

The classical zero-one law for first-order logic on random graphs says that for any first-order sentence $\phi$ in the theory of graphs, as n approaches infinity, the probability that the random graph G(n, p) satisfies $\phi$ approaches…

Let $\alpha \in (0,1)_{\mathbb{R}}$ be irrational and $G_n = G_{n,1/n^\alpha}$ be the random graph with edge probability $1/n^\alpha$; we know that it satisfies the 0-1 law for first order logic. We deal with the failure of the 0-1 law for…

We consider first order expressible properties of random perfect graphs. That is, we pick a graph $G_n$ uniformly at random from all (labelled) perfect graphs on $n$ vertices and consider the probability that it satisfies some graph…

We consider the random graph M^n_{\bar{p}} on the set [n], were the probability of {x,y} being an edge is p_{|x-y|}, and \bar{p}=(p_1,p_2,p_3,...) is a series of probabilities. We consider the set of all \bar{q} derived from \bar{p} by…

For an $n\times n$ random image with independent pixels, black with probability $p(n)$ and white with probability $1-p(n)$, the probability of satisfying any given first-order sentence tends to 0 or 1, provided both $p(n)n^{\frac{2}{k}}$…

In this work limit probabilities of first-order properties of the random $s$-uniform hypergraph in the binomial model $G^{s}(n,p)$ are studied. We give a complete discription of all positive $\alpha$ such that $G^{s}(n,n^{-\alpha})$ obeys…

In this paper the limit probabilities of first-order properties are studied. The random graph $G(n,p)$ {\it obeys Zero-One $k$-Law} if for each first-order property with quantifier depth not greater than $k$ its probability tends to 0 or…

We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed…

In this paper, we prove that for every positive $\varepsilon$, there exists an $\alpha\in(1/(k-1),1/(k-1)+\varepsilon)$ such that the binomial random graph $G(n,n^{-\alpha})$ does not obey 0-1 law w.r.t. first order sentences with k…

We study an asymptotic behavior of the probabilities of first-order properties of random graph G(N,p) in the article. We conider p such that lnp=-alnN, a>0. We find values of parameter a from (1-exp(ln2(1-k)),1) such that the random graph…

Let $G_n$ be the binomial random graph $G(n,p=c/n)$ in the sparse regime, which as is well-known undergoes a phase transition at $c=1$. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence $\phi$, the…

For a sequence p=(p(1),p(2), ...) let G(n,p) denote the random graph with vertex set {1,2, ...,n} in which two vertices i, j are adjacent with probability p(|i-j|), independently for each pair. We study how the convergence of probabilities…

We study asymptotical probabilities of first order and monadic second order properties of Erdos-Renyi random graph G(n,n^{-a}). The random graph obeys FO (MSO) zero-one k-law if for any first order (monadic second order) formulae it is true…

We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $n+1$, the vertex $n+1$ is introduced together with $m$ edges joining the new vertex with…

For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…