Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

(m,n)-cycle systems

We describe a method which, in certain circumstances, may be used to prove that the well-known necessary conditions for partitioning the edge set of the complete graph on an odd number of vertices (or the complete graph on an even number of vertices with a 1-factor removed) into cycles of lengths m(1),m(2),...,m(t) are sufficient in the case \{m(1), m(2), ..., m(t)}\=2. The method is used to settle the case where the cycle lengths are 4 and 5. (C) 1998 Elsevier Science B.V. All rights reserved.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

The metamorphosis of lambda-fold 4-wheel systems into lambda-fold 4-cycle systems

A 4-wheel is a simple graph on 5 vertices with 8 edges, formed by taking a 4-cycle and joining a fifth vertex (the centre of the 4-wheel) to each of the other four vertices. A lambda -fold 4-wheel system of order n is an edge-disjoint decomposition of the complete multigraph lambdaK(n) into 4-wheels. Here, with five isolated possible exceptions when lambda = 2, we give necessary and sufficient conditions for a lambda -fold 4-wheel system of order n to be transformed into a lambda -fold Ccyde system of order n by removing the centre vertex from each 4-wheel, and its four adjacent edges (retaining the 4-cycle wheel rim), and reassembling these edges adjacent to wheel centres into 4-cycles.

Analysis of Masticatory Cycle Efficiency in Complete Denture Wearers

Purpose: This study assessed masticatory efficiency and duration of the masticatory cycle in 14 asymptomatic patients with severe bone resorption. All patients had worn complete dentures for over 10 years. Recall visits were scheduled at 5 months and 1 year after receiving new dentures.Materials and Methods: Fourteen patients were evaluated in this study. The Research Diagnostic Criteria questionnaire and tests of the efficiency and duration of the masticatory cycle were performed with artificial food before, 5 months after, and 1 year after new dentures were delivered. Masticatory efficiency was assessed using a sieve system; artificial food was ground for 35 masticatory cycles and monitored by the operator.Results: Masticatory efficiency at 5 months was significantly improved for the 0.42-mm mesh. An improvement in masticatory efficiency and a reduction in mastication time were observed with the new dentures after 1 year.Conclusion: The results of this study indicated that 5 months did not allow enough time to demonstrate improved muscular capacity and ability after receiving new dentures. After 1 year, the duration of the masticatory cycle was reduced, and masticatory efficiency was significantly improved.

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.

Packings and coverings of the complete graph with trees

In this thesis, we define the spectrum problem for packings (coverings) of G to be the problem of finding all graphs H such that a maximum G-packing (minimum G- covering) of the complete graph with the leave (excess) graph H exists. The set of achievable leave (excess) graphs in G-packings (G-coverings) of the complete graph is called the spectrum of leave (excess) graphs for G. Then, we consider this problem for trees with up to five edges. We will prove that for any tree T with up to five edges, if the leave graph in a maximum T-packing of the complete graph Kn has i edges, then the spectrum of leave graphs for T is the set of all simple graphs with i edges. In fact, for these T and i and H any simple graph with i edges, we will construct a maximum T-packing of Kn with the leave graph H. We will also show that for any tree T with k ≤ 5 edges, if the excess graph in a minimum T-covering of the complete graph Kn has i edges, then the spectrum of excess graphs for T is the set of all simple graphs and multigraphs with i edges, except for the case that T is a 5-star, for which the graph formed by four multiple edges is not achievable when n = 12.

Complete Genome Sequence of Mycoplasma suis and Insights into Its Biology and Adaption to an Erythrocyte Niche

Mycoplasma suis, the causative agent of porcine infectious anemia, has never been cultured in vitro and mechanisms by which it causes disease are poorly understood. Thus, the objective herein was to use whole genome sequencing and analysis of M. suis to define pathogenicity mechanisms and biochemical pathways. M. suis was harvested from the blood of an experimentally infected pig. Following DNA extraction and construction of a paired end library, whole-genome sequencing was performed using GS-FLX (454) and Titanium chemistry. Reads on paired-end constructs were assembled using GS De Novo Assembler and gaps closed by primer walking; assembly was validated by PFGE. Glimmer and Manatee Annotation Engine were used to predict and annotate protein-coding sequences (CDS). The M. suis genome consists of a single, 742,431 bp chromosome with low G+C content of 31.1%. A total of 844 CDS, 3 single copies, unlinked rRNA genes and 32 tRNAs were identified. Gene homologies and GC skew graph show that M. suis has a typical Mollicutes oriC. The predicted metabolic pathway is concise, showing evidence of adaptation to blood environment. M. suis is a glycolytic species, obtaining energy through sugars fermentation and ATP-synthase. The pentose-phosphate pathway, metabolism of cofactors and vitamins, pyruvate dehydrogenase and NAD(+) kinase are missing. Thus, ribose, NADH, NADPH and coenzyme A are possibly essential for its growth. M. suis can generate purines from hypoxanthine, which is secreted by RBCs, and cytidine nucleotides from uracil. Toxins orthologs were not identified. We suggest that M. suis may cause disease by scavenging and competing for host nutrients, leading to decreased life-span of RBCs. In summary, genome analysis shows that M. suis is dependent on host cell metabolism and this characteristic is likely to be linked to its pathogenicity. The prediction of essential nutrients will aid the development of in vitro cultivation systems.

A family of perfect factorisations of complete bipartite graphs

A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n = p(2) for an odd prime p. We construct a family of (p-1)/2 non-isomorphic perfect 1-factorisations of K-n,K-n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltoilian if the permutation defined by any row relative to any other row is a single Cycle. (C) 2002 Elsevier Science (USA).

2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only

It is shown that quasigroups constructed using the standard construction from 2-perfect directed m-cycle systems are precisely the finite members of a variety if and only if m=3, 4 or 5.

2m-cycle systems of K2m+1/C-m

For all m greater than or equal to 3 the edges of complete graph on 2m + 1 vertices can he partitioned into m 2m-cycles and an m-cycle.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

New low-power 1.5-bit time-interleaved MDAC based on MOS capacitor amplification

15th IEEE International Conference on Electronics, Circuits and Systems, Malta