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The Chromatic Numbers of Random Hypergraphs
 Random Struct. Alg
, 1998
"... : For a pair of integers 1### r, the #chromatic number of an runiform Z. hypergraph H# V, E is the minimal k, for which there exists a partition of V into subsets ## T,...,T such that e#T ## for every e#E. In this paper we determine the asymptotic 1 ki Z. behavior of the #chromatic number of t ..."
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Cited by 2 (1 self)
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: For a pair of integers 1### r, the #chromatic number of an runiform Z. hypergraph H# V, E is the minimal k, for which there exists a partition of V into subsets ## T,...,T such that e#T ## for every e#E. In this paper we determine the asymptotic 1 ki Z. behavior of the #chromatic number
Choosability in Random Hypergraphs
 J. Comb. Theory Ser. B
"... The choice number of a hypergraph H = (V; E) is the least integer s for which for every family of color lists S = fS(v) : v 2 V g, satisfying jS(v)j = s for every v 2 V , there exists a choice function f so that f(v) 2 S(v) for every v 2 V , and no edge of H is monochromatic under f . In this paper ..."
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Cited by 9 (2 self)
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we consider the asymptotic behavior of the choice number of a random kuniform hypergraph H(k; n; p). Our main result states that for every k 2 and for all values of the edge probability p = p(n) down to p = O(n k+1 ) the ratio between the choice number and the chromatic number of H(k; n; p) does
A RiskFactor Model Foundation for RatingsBased Bank Capital Rules
 Journal of Financial Intermediation
, 2003
"... When economic capital is calculated using a portfolio model of credit valueatrisk, the marginal capital requirement for an instrument depends, in general, on the properties of the portfolio in which it is held. By contrast, ratingsbased capital rules, including both the current Basel Accord and i ..."
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Cited by 283 (1 self)
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risk factor driving correlations across obligors, and (b) no exposure in a portfolio accounts for more than an arbitrarily small share of total exposure. Analysis of rates of convergence to asymptotic VaR leads to a simple and accurate portfoliolevel addon charge for undiversified idiosyncratic risk
Asymptotics of Hypergraph Matching, Covering and Coloring Problems
"... A hypergraph H is simply a collection of subsets of a finite set, which we will always denote by V. Elements of V are called vertices and elements of H edges. A hypergraph is kuniform (kbounded) if each of its edges has size k (at most k). The degree in H of a vertex x is the number of edges conta ..."
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A hypergraph H is simply a collection of subsets of a finite set, which we will always denote by V. Elements of V are called vertices and elements of H edges. A hypergraph is kuniform (kbounded) if each of its edges has size k (at most k). The degree in H of a vertex x is the number of edges
A Comparison of Dynamic Branch Predictors that use Two Levels of Branch History
 in Proceedings of the 20th Annual International Symposium on Computer Architecture
, 1993
"... Recent attention to speculative execution as a mechanism for increasing performance of single instruction streams has demanded substantially better branch prediction than what has been previously available. We [1, 2] and Pan, So, and Rahmeh [4] have both proposed variations of the same aggressive dy ..."
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Cited by 279 (9 self)
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Recent attention to speculative execution as a mechanism for increasing performance of single instruction streams has demanded substantially better branch prediction than what has been previously available. We [1, 2] and Pan, So, and Rahmeh [4] have both proposed variations of the same aggressive dynamic branch predictor for handling those needs. We call the basic model TwoLevel Adaptive Branch Prediction; Pan, So, and Rahmeh call it Correlation Branch Prediction. In this paper, we adopt the terminology of [2] and show that there are really nine variations of the same basic model. We compare the nine variations with respect to the amount of history information kept. We study the effects of different branch history lengths and pattern history table configurations. Finally, we evaluate the cost effectiveness of the nine variations. 1 Introduction With the current movement toward deeper pipelines and wider issue rates, extremely high branch prediction accuracy becomes critical because a...
ON THE CHROMATIC NUMBER OF GEOMETRIC HYPERGRAPHS
 VOL. 21, NO. 3, PP. 676–687
, 2007
"... A finite family R of simple Jordan regions in the plane defines a hypergraph H = H(R) where the vertex set of H is R and the hyperedges are all subsets S ⊂Rfor which there is a point p such that S = {r ∈Rp ∈ r}. The chromatic number of H(R) is the minimum number of colors needed to color the membe ..."
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Cited by 3 (0 self)
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A finite family R of simple Jordan regions in the plane defines a hypergraph H = H(R) where the vertex set of H is R and the hyperedges are all subsets S ⊂Rfor which there is a point p such that S = {r ∈Rp ∈ r}. The chromatic number of H(R) is the minimum number of colors needed to color
On the chromatic number of Kneser hypergraphs
, 2000
"... We give a simple and elementary proof of Kr'iz's lower bound on the chromatic number of the Kneser rhypergraph of a set system S. ..."
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Cited by 5 (1 self)
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We give a simple and elementary proof of Kr'iz's lower bound on the chromatic number of the Kneser rhypergraph of a set system S.
Hypergraphs with Zero Chromatic Threshold
, 1307
"... Let F be an runiform hypergraph. The chromatic threshold of the family of Ffree, runiform hypergraphs is the infimum of all nonnegative reals c such that the subfamily of Ffree, runiform hypergraphs H with minimum degree at least c (V(H)) r−1 has bounded chromatic number. The study of chroma ..."
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Let F be an runiform hypergraph. The chromatic threshold of the family of Ffree, runiform hypergraphs is the infimum of all nonnegative reals c such that the subfamily of Ffree, runiform hypergraphs H with minimum degree at least c (V(H)) r−1 has bounded chromatic number. The study
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126,097