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» Parameterizing by the Number of Numbers
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149
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COMBINATORICS
2007
121views more  COMBINATORICS 2007»
15 years 6 months ago
A Bound for Size Ramsey Numbers of Multi-partite Graphs
It is shown that the (diagonal) size Ramsey numbers of complete m-partite graphs Km(n) can be bounded from below by cn22(m−1)n, where c is a positive constant. Key words: Size R...
Yuqin Sun, Yusheng Li
147
Voted
COMBINATORICS
2000
87views more  COMBINATORICS 2000»
15 years 5 months ago
Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers
We give new lower bounds for the Schur numbers S(6) and S(7). This will imply new lower bounds for the Multicolor Ramsey Numbers R6(3) and R7(3). We also make several observations...
Harold Fredricksen, Melvin M. Sweet
175
Voted
DM
1998
118views more  DM 1998»
15 years 5 months ago
Chromatic Ramsey numbers
Suppose G is a graph. The chromatic Ramsey number rc(G) of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true: For any...
Xuding Zhu
143
Voted
JC
2010
95views more  JC 2010»
15 years 4 months ago
Stochastic perturbations and smooth condition numbers
In this paper we dene a new condition number adapted to directionally uniform perturbations in a general framework of maps between Riemannian manifolds. The denitions and theorem...
Diego Armentano
178
Voted
MCS
2010
Springer
16 years 23 days ago
Estimation of the Number of Clusters Using Multiple Clustering Validity Indices
One of the challenges in unsupervised machine learning is finding the number of clusters in a dataset. Clustering Validity Indices (CVI) are popular tools used to address this pro...
Krzysztof Kryszczuk, Paul Hurley