On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Degree Sums and Covering Cycles

It is shown that if in a simple graph G of order n the sum of degrees of any three pairwise non-adjacent vertices is at least n, then there are two cycles (or one cycle and an edge or a vertex) of GF that contain all the vertices. © 1995 John Wiley & Sons, Inc.     

Contractions and minimalk-colorability

Coloring the vertex set of a graphG with positive integers, thechromatic sum (G) ofG is the minimum sum of colors in a proper coloring. Thestrength ofG is the largest integer that occurs in every coloring whose total is(G). Proving a conjecture of Kubicka and Schwenk, we show that every tree of strengths has at least ((2 + ) ^s–1 – (2 – ) ^s–1)/ vertices (s 2). Surprisingly, this extremal result follows from a topological property of trees. Namely, for everys 3 there exist precisely two treesT _s andR _s such that every tree of strength at leasts is edge-contractible toT _s orR _s .     

Sub-Ramsey numbers for arithmetic progressions

Letm 3 andk 1 be two given integers. Asub-k-coloring of [n] = {1, 2,...,n} is an assignment of colors to the numbers of [n] in which each color is used at mostk times. Call an arainbow set if no two of its elements have the same color. Thesub-k-Ramsey number sr(m, k) is defined as the minimumn such that every sub-k-coloring of [n] contains a rainbow arithmetic progression ofm terms. We prove that((k – 1)m ²/logmk) sr(m, k) O((k – 1)m ² logmk) asm , and apply the same method to improve a previously known upper bound for a problem concerning mappings from [n] to [n] without fixed points.Research supported in part by Allon Fellowship and by a Bat Sheva de-Rothschild grant.Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences, grant No. 1-3-86-264.     

Haplotyping by capillary electrophoresis

The investigation of the genetic background and phenotype structures of complex diseases, such as cardiovascular or psychiatric disorders and tumors, is one of the most scrutinized fields of the post genomic era. Besides the multiplex analysis of genetic markers and polymorphisms throughout the whole genome, more and more attention is focused on the interaction between the etiological factors of these traits. Haplotype determination, rather than multiplex genotyping seems to be one of the first building blocks of this endeavor. This review focuses on the importance and theoretical background of haplotyping, and summarizes the recent examples of novel and emerging haplotyping techniques by capillary gel electrophoresis based DNA fragment analysis, a powerful tool for the examination of the inheritance of complex traits.     

Cellulose production based on hemicellulose hydrolysate from steam-pretreated willow

The production cost of cellulolytic enzymes is a major contributor to the high cost of ethanol production from lignocellulosics using enzymatic hydrolysis. The aim of the present study was to investigate the cellulolytic enzyme production ofTrichoderma reesei Rut C 30, which is known as a good cellulase secreting micro-organism, using willow as the carbon source. The willow, which is a fast-growing energy crop in Sweden, was impregnated with 1–4% SO₂ and steam-pretreated for 5 min at 206°C. The pretreated willow was washed and the wash water, which contains several soluble sugars from the hemicellulose, was supplemented with fibrous pretreated willow and used for enzyme production. In addition to sugars, the liquid contains degradation products such as acetic acid, furfural, and 5-hydroxy-methylfurfural, which are inhibitory for microorganisms. The results showed that 50% of the cellulose can be replaced with sugars from the wash water. The highest enzyme activity, 1.79 FPU/mL and yield, 133 FPU/g carbohydrate, was obtained at pH 6.0 using 20 g/L carbon source concentration. At lower pHs, a total lack of growth and enzyme production was observed, which probably could be explained by furfural inhibition.     

Advances in inorganic chemistry and radiochemistry,vol. 18: Edited by H.J. Emeléus and A.G. Sharpe,Academic Press,New York/San Francisco/London, 1976, vii + 414 pages, $35.50.

The catinic complex trans-[FeCl(CCHPh)(depe)₂]⁺ (depe = bis(diethylphosphino)ethane has been prepared by interaction of trans-[FeCl₂(depe)₂] with penylacetylene in methanol solution in the presence of NaX (X = BPh₄ or PF₆.