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RSA
2008
118views more  RSA 2008»
14 years 9 months ago
The cover time of the giant component of a random graph
We study the cover time of a random walk on the largest component of the random graph Gn,p. We determine its value up to a factor 1 + o(1) whenever np = c > 1, c = O(ln n). In ...
Colin Cooper, Alan M. Frieze
LATIN
2004
Springer
15 years 2 months ago
Embracing the Giant Component
Consider a game in which edges of a graph are provided a pair at a time, and the player selects one edge from each pair, attempting to construct a graph with a component as large ...
Abraham Flaxman, David Gamarnik, Gregory B. Sorkin
COMBINATORICA
2007
129views more  COMBINATORICA 2007»
14 years 9 months ago
Birth control for giants
The standard Erd˝os-Renyi model of random graphs begins with n isolated vertices, and at each round a random edge is added. Parametrizing n 2 rounds as one time unit, a phase tra...
Joel H. Spencer, Nicholas C. Wormald
WAW
2007
Springer
120views Algorithms» more  WAW 2007»
15 years 3 months ago
Giant Component and Connectivity in Geographical Threshold Graphs
The geographical threshold graph model is a random graph model with nodes distributed in a Euclidean space and edges assigned through a function of distance and node weights. We st...
Milan Bradonjic, Aric A. Hagberg, Allon G. Percus
78
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CPC
1998
123views more  CPC 1998»
14 years 9 months ago
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Given a sequence of non-negative real numbers 0 1 ::: which sum to 1, we consider a random graph having approximately in vertices of degree i. In 12] the authors essentially show ...
Michael Molloy, Bruce A. Reed