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SODA
2012
ACM
213views Algorithms» more  SODA 2012»
6 years 10 months ago
Expanders are universal for the class of all spanning trees
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...
INFOCOM
2012
IEEE
6 years 10 months ago
Impact of power-law topology on IP-level routing dynamics: Simulation results
—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...
Amelie Medem Kuatse, Clémence Magnien, Fabi...
CSR
2011
Springer
7 years 12 months ago
The Complexity of Inversion of Explicit Goldreich's Function by DPLL Algorithms
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...
Dmitry Itsykson, Dmitry Sokolov
SIAMDM
2010
110views more  SIAMDM 2010»
8 years 3 months ago
Embedding Spanning Trees in Random Graphs
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...
Michael Krivelevich
JCT
2010
127views more  JCT 2010»
8 years 3 months ago
On the density of a graph and its blowup
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 ...
Asaf Shapira, Raphael Yuster
RSA
2011
121views more  RSA 2011»
8 years 3 months ago
Ramsey games with giants
: 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...
RSA
2011
124views more  RSA 2011»
8 years 3 months ago
Sparse random graphs with clustering
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...
Béla Bollobás, Svante Janson, Oliver...
COMBINATORICA
2010
8 years 5 months ago
Online vertex-coloring games in random graphs
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...
Martin Marciniszyn, Reto Spöhel
ISAAC
2010
Springer
266views Algorithms» more  ISAAC 2010»
8 years 6 months ago
Structural and Complexity Aspects of Line Systems of Graphs
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 ...
Jozef Jirásek, Pavel Klavík
RSA
2010
104views more  RSA 2010»
8 years 6 months ago
Random graphs with forbidden vertex degrees
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...
Geoffrey R. Grimmett, Svante Janson
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