Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

Steiner triple systems with two disjoint subsystems

It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order v by removing the edges of two vertex disjoint complete subgraphs of orders u and w if and only if u, w, and v are odd, ((v)(2)) - ((u)(2)) - ((w)(2)) equivalent to 0 (mod 3), and v >= w + u + max {u, w}. Such decompositions are equivalent to group divisible designs with block size 3, one group of size u, one group of size w, and v - u - w groups of size 1. This result settles the existence problem for Steiner triple systems having two disjoint specified subsystems, thereby generalizing the well-known theorem of Doyen and Wilson on the existence of Steiner triple systems with a single specified subsystem. (c) 2005 Wiley Periodicals, Inc.

A generalization of Ramsey theory for graphs, with stars and complete graphs as forbidden subgraphs /

Includes bibliographical references.

The extended metamorphosis of a complete bipartite design into a cycle system

A K-t,K-t-design of order n is an edge-disjoint decomposition of K-n into copies of K-t,K-t. When t is odd, an extended metamorphosis of a K-t,K-t-design of order n into a 2t-cycle system of order n is obtained by taking (t - 1)/2 edge-disjoint cycles of length 2t from each K-t,K-t block, and rearranging all the remaining 1-factors in each K-t,K-t block into further 2t-cycles. The 'extended' refers to the fact that as many subgraphs isomorphic to a 2t-cycle as possible are removed from each K-t,K-t block, rather than merely one subgraph. In this paper an extended metamorphosis of a K-t,K-t-design of order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is given for all odd t > 3. A metamorphosis of a 2-fold K-t,K-t-design of any order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is also given, for all odd t > 3. (The case t = 3 appeared in Ars Combin. 64 (2002) 65-80.) When t is even, the graph K-t,K-t is easily seen to contain t/2 edge-disjoint cycles of length 2t, and so the metamorphosis in that case is straightforward. (C) 2004 Elsevier B.V. All rights reserved.

Constraints on the complete optimization of human motion

In sport and exercise biomechanics, forward dynamics analyses or simulations have frequently been used in attempts to establish optimal techniques for performance of a wide range of motor activities. However, the accuracy and validity of these simulations is largely dependent on the complexity of the mathematical model used to represent the neuromusculoskeletal system. It could be argued that complex mathematical models are superior to simple mathematical models as they enable basic mechanical insights to be made and individual-specific optimal movement solutions to be identified. Contrary to some claims in the literature, however, we suggest that it is currently not possible to identify the complete optimal solution for a given motor activity. For a complete optimization of human motion, dynamical systems theory implies that mathematical models must incorporate a much wider range of organismic, environmental and task constraints. These ideas encapsulate why sports medicine specialists need to adopt more individualized clinical assessment procedures in interpreting why performers' movement patterns may differ.

Phylogenetic analysis of polyomaviruses based on their complete genomes

Perez-Losada et al. [1] analyzed 72 complete genomes corresponding to nine mammalian (67 strains) and 2 avian (5 strains) polyomavirus species using maximum likelihood and Bayesian methods of phylogenetic inference. Because some data of 2 genomes in their work are now not available in GenBank, in this work, we analyze the phylogenetic relationship of the remaining 70 complete genomes corresponding to nine mammalian (65 strains) and two avian (5 strains) polyomavirus species using a dynamical language model approach developed by our group (Yu et al., [26]). This distance method does not require sequence alignment for deriving species phylogeny based on overall similarities of the complete genomes. Our best tree separates the bird polyomaviruses (avian polyomaviruses and goose hemorrhagic polymaviruses) from the mammalian polyomaviruses, which supports the idea of splitting the genus into two subgenera. Such a split is consistent with the different viral life strategies of each group. In the mammalian polyomavirus subgenera, mouse polyomaviruses (MPV), simian viruses 40 (SV40), BK viruses (BKV) and JC viruses (JCV) are grouped as different branches as expected. The topology of our best tree is quite similar to that of the tree constructed by Perez-Losada et al.

Complete Nucleotide Sequence of Rice Tungro Spherical Virus Genome of a Highly Virulent Strain Vt6

The complete nucleotide sequence of rice tungro spherical virus (RTSV) strain Vt6, originally from Mindanao, the Philippines, with higher virulence to resistant rice cultivars, was determined and compared with the published sequence for the Philippine-type strain A (RTSV-A-Shen). It was reported that RTSV-A was not able to infect a rice resistant cultivar TKM 6 (10). RTSV-Vt6 and RTSV-A-Shen share 90% and 95% homology at nucleotide and amino-acid levels, respectively. The N-terminal leader sequence of RTSV-Vt6 contained a 39-amino acids-region (positions 65 to 103) which was totally different from that of RTSV-A-Shen; the difference resulted from frame shifting by nucleotide insertions and deletions. To confirm the amino-acid sequence differences of the leader polypeptide, the same region was cloned and sequenced using a newly obtained variant of RTSV-type 6, which had been collected in the field of IRRI, and seven field isolates from Mindanao, the Philippines. Since all the sequences of the target region are identical to that of the Vt6 leader polypeptide, the sequence difference in the leader region seems not to correlate with the virulence of Vt6.

Towards more complete satisfaction of customers in construction

In an environment where economic, political and technological change is the rule, a fundamental business strategy should be the defence of traditional markets and thoughtful entry into new markets, with an aim to increase market penetration and stimulate profit. The success of such a strategy will depend on the success of firms to do more and better for customers than their competitors. In other words, the firm’s primary competitive advantage will come from changes they implement to please their customers. In the construction industry, complexity of technical knowledge and construction processes have traditionally encouraged clients to play a largely passive role in the management of their project. However, today’s clients not only want to know about internal efficiency of their projects but also need to know how they and their contractors compare and compete against their competitors. Given the vulnerability of construction activities in the face of regional financial crisis, constructors need to be proactive in the search to improve their internal firm and project processes to ensure profitability and market responsiveness. In this context, reengineering is a radical design that emphasises customer satisfaction rather than cost reduction This paper discusses the crucial role of the client-project interface and how project networks could facilitate and improve information dissemination and sharing, collaborative efforts, decision-making and improved project climate. An intra-project network model is presented, and project managers’ roles and competencies in forming and coordinating project workgroups is discussed.