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» The b-chromatic Number of a Graph
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STOC
2004
ACM
134views Algorithms» more  STOC 2004»
14 years 7 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 1 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 29 days 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
BMCBI
2010
86views more  BMCBI 2010»
13 years 7 months ago
Reaction graph kernels predict EC numbers of unknown enzymatic reactions in plant secondary metabolism
Background: Understanding of secondary metabolic pathway in plant is essential for finding druggable candidate enzymes. However, there are many enzymes whose functions are not yet...
Hiroto Saigo, Masahiro Hattori, Hisashi Kashima, K...
JUCS
2006
94views more  JUCS 2006»
13 years 7 months ago
Completeness in the Boolean Hierarchy: Exact-Four-Colorability, Minimal Graph Uncolorability, and Exact Domatic Number Problems
: This paper surveys some of the work that was inspired by Wagner's general technique to prove completeness in the levels of the boolean hierarchy over NP and some related res...
Tobias Riege, Jörg Rothe