C4-saturated bipartite graphs

Let H be a graph. A graph G is said to be H-free if it contains no subgraph isomorphic to H. A graph G is said to be an H-saturated subgraph of a graph K if G is an H-free subgraph of K with the property that for any edge e is an element of E(K)\E(G), G boolean OR {e} is not H-free. We present some general results on K-s,K-t-saturated subgraphs of the complete bipartite graph K-m,K-n and study the problem of finding, for all possible values of q, a C-4-saturated subgraph of K., having precisely q edges. (C) 2002 Elsevier Science B.V. All rights reserved.

The human melanocortin-1 receptor locus: analysis of transcription unit, locus polymorphism and haplotype evolution

The complete sequence of the MCIR locus has been assembled, the coding region of the gene is intronless and placed within a 12 kb region flanked by the NULP1 and TUBB4 genes. The immediate promoter region has an E-box site with homology to the M-box consensus known to bind the microphthalmia transcription factor (MITF), however, promoter deletion analysis and transactivation studies have failed to show activation through this element by MITF. Polymorphism within the coding region, immediate 5' promoter region and a variable number tandem repeat (VNTR) minisatellite within the locus have been examined in a collection of Caucasian families and African individuals. Haplotype analysis shows linkage disequilibrium between the VNTR and MCIR coding region red hair variant alleles which can be used to estimate the age of these missense changes. Assuming a mean VNTR mutation rate of 1% and a star phylogeny, we estimate the Arg151Cys variant arose 7500 years before the present day, suggesting these variants may have arisen in the Caucasian population more recently than previously thought. (C) 2001 Published by Elsevier Science B.V.

An automated multi-unit composting facility for biodegradability evaluations

A system has been developed for studying the biodegradation of natural and synthetic polymeric material. The system is based on standard methods developed by the European Committee for Standardisation (CEN TC 261) (ISO/DIS 14855) and the American Society of Testing Materials, 'ASTM. Standard Test Method for Determining Aerobic. Biodegradation of Plastic Materials under Controlled Composting Conditions' (ASTM D 5338-92). A new low-cost compost facility has been used which satisfies the requirements of these standards. The system has been automated for data collection and has been run under the conditions specified by the standards. In the system, cellulose, newspaper and two starch-based polymers were treated with compost in a series of 3dm(3) vessels at 52 degreesC and under conditions of optimum moisture and pH. The degradation was followed over time by measuring the amount of carbon released as carbon dioxide. (C) 2001 Society of Chemical Industry.

Trade spectra of complete partite graphs

The trade spectrum of a graph G is essentially the set of all integers t for which there is a graph H whose edges can be partitioned into t copies of G in two entirely different ways. In this paper we determine the trade spectrum of complete partite graphs, in all but a few cases.

Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.

Further decompositions of complete tripartite graphs into 5-cycles

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r less than or equal to s less than or equal to t. Necessary and sufficient conditions are given for decomposability of K(r, s, t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirza-khani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235-241) and Cavenagh and Billington. (C) 2002 Elsevier Science B.V. All rights reserved.