for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.

Determining the number of clusters present in a dataset is an important problem cluster analysis. Conventional clustering techniques generally assume this parameter to be provided up front. %user supplied. %Recently, robustness any given algorithm analyzed measure stability/instability which turn determines number. In paper, we propose method analyzes stability for predicting Under same computa...

Having based on the analysis of Pietronero and collaborators the galaxy number counts can be considered as an evidence of that the geometry of the universe is euclidean and that the K-corrections are absent. In such a universe measuring the cosmological redshift of the object and measuring the flux from the object are inconsistent. It is considered the model of the universe which describes the ...

Let K n denote the Cartesian product Kn Kn Kn, where Kn is the complete graph on n vertices. We show that the domination number of K n is ⌈