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JCT
2011
90views more  JCT 2011»
14 years 9 months ago
Small subgraphs in random graphs and the power of multiple choices
The standard paradigm for online power of two choices problems in random graphs is the Achlioptas process. Here we consider the following natural generalization: Starting with G0 a...
Torsten Mütze, Reto Spöhel, Henning Thom...
IM
2008
15 years 2 months ago
Directed Random Dot Product Graphs
In this paper we consider three models for random graphs that utilize the inner product as their fundamental object. We analyze the behavior of these models with respect to cluster...
Stephen J. Young, Edward R. Scheinerman
SPAA
1993
ACM
15 years 6 months ago
Optimal Parallel Construction of Hamiltonian Cycles and Spanning Trees in Random Graphs
We give tight bounds on the parallel complexity of some problems involving random graphs. Speci cally, we show that a Hamiltonian cycle, a breadth rst spanning tree, and a maximal...
Philip D. MacKenzie, Quentin F. Stout
ENDM
2007
74views more  ENDM 2007»
15 years 2 months ago
The order of the largest complete minor in a random graph
Let ccl(G) denote the order of the largest complete minor in a graph G (also called the contraction clique number) and let Gn,p denote a random graph on n vertices with edge probab...
Nikolaos Fountoulakis, Daniela Kühn, Deryk Os...
STOC
2004
ACM
110views Algorithms» more  STOC 2004»
16 years 2 months ago
On sums of independent random variables with unbounded variance, and estimating the average degree in a graph
We prove the following inequality: for every positive integer n and every collection X1, . . . , Xn of nonnegative independent random variables that each has expectation 1, the pr...
Uriel Feige