Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs ...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa...
—This paper focuses on the Internet IP-level routing topology and proposes relevant explanations to its apparent dynamics. We first represent this topology as a power-law random...
The Goldreich’s function has n binary inputs and n binary outputs. Every output depends on d inputs and is computed from them by the fixed predicate of arity d. Every Goldreich...
We prove that if T is a tree on n vertices with maximum degree and the edge probability p(n) satisfies: np C max{ log n, n } for some constant > 0, then with high probability...
It is well-known that, of all graphs with edge-density p, the random graph G(n, p) contains the smallest density of copies of Kt,t, the complete bipartite graph of size 2t. Since ...
: The classical result in the theory of random graphs, proved by Erd˝os and Rényi in 1960, concerns the threshold for the appearance of the giant component in the random graph pr...
Tom Bohman, Alan M. Frieze, Michael Krivelevich, P...
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edge...
Consider the following one-player game. The vertices of a random graph on n vertices are revealed to the player one by one. In each step, also all edges connecting the newly reveal...
We study line systems in metric spaces induced by graphs. A line is a subset of vertices defined by a relation of betweeness. We show that the class of all graphs having exactly k ...
We study the random graph Gn,λ/n conditioned on the event that all vertex degrees lie in some given subset S of the nonnegative integers. Subject to a certain hypothesis on S, the...