Monochromatic Clique Decompositions of Graphs

Let $G$ be a graph whose edges are coloured with $k$ colours, and $\mathcal H=(H_1,\dots , H_k)$ be a $k$-tuple of graphs. A monochromatic $\mathcal H$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\le i\le k$. Let $\phi_{k}(n,\mathcal H)$ be the smallest number $\phi$, such that, for every order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\mathcal H$-decomposition with at most $\phi$ elements. Extending the previous results of Liu and Sousa ["Monochromatic $K_r$-decompositions of graphs", Journal of Graph Theory}, 76:89--100, 2014], we solve this problem when each graph in $\mathcal H$ is a clique and $n\ge n_0(\mathcal H)$ is sufficiently large.Comment: 14 pages; to appear in J Graph Theor

Monitoring GRID resources: JMX in action

This paper summarizes research on monitoring GRID resources, which resulted in the implementation of the JIMS system. It contains an overview of the most important architectural and software concepts that make the constructed system flexible and user-friendly. The paper evaluates JMX and Web Service technologies as foundations for implementing monitoring systems. Particular attention has been paid to system adaptability, autoconfiguration and interoperability

On the covering of t-sets with (t + 1)-sets:C(9, 5, 4) and C(10, 6, 5)

A (υ, k, t) covering system is a pair (X, B) where X is a υ-set of points and B is a family of k-subsets, called blocks, of X such that every t-subset of X is contained in at least one block. The minimum possible number of blocks in a (υ, k, t) covering system is denoted by C(υ, k, t). It is proven that there are exactly three non-isomorphic systems giving C(9, 5, 4) = 30, and a unique system giving C(10, 6, 5) = 50. © 1991

The Parameters 4-(12,6,6) and Related t-Designs

It is shown that a 4-(12,6,6) design, if it exists, must be rigid. The intimate relationship of such a design with 4-(12,5,4) designs and 5-(12,6,3) designs is presented and exploited. In this endeavor we found: (i) 30 nonisomorphic 4-(12,5,4) designs; (ii) all cyclic 3-(11,5,6) designs; (iii) all 5-(12,6,3) designs preserved by an element of order three fixing no points and no blocks; and (iv) all 5-(12,6,3) designs preserved by an element of order two fixing 2 points. 1 Introduction A simple t\Gamma(v; k; ) design is a pair (X; D) where X is a v-element set of points and D is a collection of distinct k-element subsets of X called blocks such that: for all T ae X, jT j = t, jfK 2 D : T ae Kgj = . For v 12, 4-(12,6,6) is the only parameter case for which existence is unsettled. It is known that necessary conditions for the existence of a t\Gamma(v; k; ) design are that for each 0 i t / v \Gamma i t \Gamma i ! j 0 (modulo / k \Gamma i t \Gamma i ! ): Given integers 0 t ..