Add to ORKGFor any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is further extended to $\mathcal{G}_{{\bf d}}$, the probability space of random graphs with a given degree sequence $\bf d$
AbstractIn this work we show that with high probability the chromatic number of a graph sampled from...
In this work we determine the expected number of vertices of degree k = k(n) in a graph with n verti...
AbstractWe consider the size of the largest induced tree in random graphs, random regular graphs and...
AbstractLet Gn,d denote the uniformly random d-regular graph on n vertices. For any S⊂[n], we obtain...
For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced ...
AbstractThe main aim of this short paper is to answer the following question. Given a fixed graph H,...
We improve the estimates of the subgraph probabilities in a random regular graph. Using the improved...
AbstractLet Gn be a graph selected at random from the set of all labeled graphs of order n. We show ...
For the Erdős–Rényi random graph Gn,p, we give a precise asymptotic formula for the size â1(Gn,p) of...
We describe a general approach of determining the distribution of spanning subgraphs in the random g...
AbstractThe random graph Kn,p is constructed on n labelled vertices by inserting each of the (n2) po...
Let GD be the set of graphs G(V, E) with n vertices, and the degree sequence equal to D = (d1, d2,.....
Let H be a fixed graph and math formula a subcritical graph class. In this paper we show that the nu...
For the Erdős–Rényi random graph Gn,pGn,p, we give a precise asymptotic formula for the size αˆt(Gn,...
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the s...
AbstractIn this work we show that with high probability the chromatic number of a graph sampled from...
In this work we determine the expected number of vertices of degree k = k(n) in a graph with n verti...
AbstractWe consider the size of the largest induced tree in random graphs, random regular graphs and...
AbstractLet Gn,d denote the uniformly random d-regular graph on n vertices. For any S⊂[n], we obtain...
For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced ...
AbstractThe main aim of this short paper is to answer the following question. Given a fixed graph H,...
We improve the estimates of the subgraph probabilities in a random regular graph. Using the improved...
AbstractLet Gn be a graph selected at random from the set of all labeled graphs of order n. We show ...
For the Erdős–Rényi random graph Gn,p, we give a precise asymptotic formula for the size â1(Gn,p) of...
We describe a general approach of determining the distribution of spanning subgraphs in the random g...
AbstractThe random graph Kn,p is constructed on n labelled vertices by inserting each of the (n2) po...
Let GD be the set of graphs G(V, E) with n vertices, and the degree sequence equal to D = (d1, d2,.....
Let H be a fixed graph and math formula a subcritical graph class. In this paper we show that the nu...
For the Erdős–Rényi random graph Gn,pGn,p, we give a precise asymptotic formula for the size αˆt(Gn,...
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the s...
AbstractIn this work we show that with high probability the chromatic number of a graph sampled from...
In this work we determine the expected number of vertices of degree k = k(n) in a graph with n verti...
AbstractWe consider the size of the largest induced tree in random graphs, random regular graphs and...