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SODA

2012

ACM

6 years 10 months ago
2012

ACM

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 ...

INFOCOM

2012

IEEE

6 years 10 months ago
2012

IEEE

—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...

CSR

2011

Springer

7 years 12 months ago
2011

Springer

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...

SIAMDM

2010

8 years 3 months ago
2010

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...

JCT

2010

8 years 3 months ago
2010

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 ...

RSA

2011

8 years 3 months ago
2011

: 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...

RSA

2011

8 years 3 months ago
2011

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...

COMBINATORICA

2010

8 years 5 months ago
2010

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...

ISAAC

2010

Springer

8 years 6 months ago
2010

Springer

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 ...

RSA

2010

8 years 6 months ago
2010

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...