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SODA

2012

ACM

8 years 6 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

8 years 6 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

9 years 7 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

9 years 11 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

9 years 11 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

9 years 11 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

9 years 11 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

10 years 1 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

10 years 2 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

10 years 2 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...