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APPROX
2004
Springer
179views Algorithms» more  APPROX 2004»
14 years 2 months ago
Maximum Weight Independent Sets and Matchings in Sparse Random Graphs. Exact Results Using the Local Weak Convergence Method
ABSTRACT: Let G(n, c/n) and Gr(n) be an n-node sparse random graph and a sparse random rregular graph, respectively, and let I(n, r) and I(n, c) be the sizes of the largest indepen...
David Gamarnik, Tomasz Nowicki, Grzegorz Swirszcz
STOC
2004
ACM
134views Algorithms» more  STOC 2004»
14 years 9 months ago
The two possible values of the chromatic number of a random graph
Given d (0, ) let kd be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n, d/n) is either kd or kd + 1 almost surely.
Dimitris Achlioptas, Assaf Naor
ICALP
2007
Springer
14 years 3 months ago
On the Chromatic Number of Random Graphs
In this paper we consider the classical Erd˝os-R´enyi model of random graphs Gn,p. We show that for p = p(n) ≤ n−3/4−δ , for any fixed δ > 0, the chromatic number χ...
Amin Coja-Oghlan, Konstantinos Panagiotou, Angelik...
APPROX
2004
Springer
129views Algorithms» more  APPROX 2004»
14 years 2 months ago
The Chromatic Number of Random Regular Graphs
Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1...
Dimitris Achlioptas, Cristopher Moore
TIP
2008
124views more  TIP 2008»
13 years 9 months ago
Graph Laplacian Tomography From Unknown Random Projections
We introduce a graph Laplacian based algorithm for the tomography reconstruction of a planar object from its projections taken at random unknown directions. The algorithm is shown ...
Ronald R. Coifman, Yoel Shkolnisky, Fred J. Sigwor...