Ramsey Goodness of Bounded Degree Trees

Given a pair of graphs G and H, the Ramsey number R(G, H) is the smallest N such that every red-blue coloring of the edges of the complete graph KN contains a red copy of G or a blue copy of H. If a graph G is connected, it is well known and easy to show that R(G, H) ≥ (|G| − 1)(χ(H) − 1) + σ(H), where χ(H) is the chromatic number of H and σ(H) is the size of the smallest color class in a χ(H)-coloring of H. A graph G is called H-good if R(G, H) = (|G| − 1)(χ(H) − 1) + σ(H). The notion of Ramsey goodness was introduced by Burr and Erd˝os in 1983 and has been extensively studied since then. In this paper we show that if n ≥ Ω(|H| log4 |H|) then every n-vertex bounded degree tree T is H-good. The dependency between n and |H| is tight up to log factors. This substantially improves a result of Erd˝os, Faudree, Rousseau, and Schelp from 1985, who proved that n-vertex bounded degree trees are H-good when n ≥ Ω(|H| 4 ). MSC: 05C05, 05C5

A remark on Hamilton cycles with few colors

Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of Kn with n colours contains a Hamilton cycle with ≤O(logn) colours. They proved that there is always a Hamilton cycle with ≤8n−−√ colours. In this note we improve this bound to O(log3n)

Method and Experimental Setup for the Study of the Local Current Distribution in Conducting Micro-and Nanostructures

The method for the study of the spatial distribution of current in micro-and nanostructures on the measured magnetic field is presented. The methods of studies the magnetic field distribution of conducting nanostructures by passing a transport current are considered. The technique of current recovery from experimental data is offered. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3522

Dyssynchrony of the heart as a pathogenetic mechanism of the chronic cardiac insufficiency progression on the backgroound of ischemic heart disease or physiological aging of the heart

This publication covers the mechanisms of fibrous remodeling of the aging heart, formation of the fibrosis and dyssynchrony. There are presented the information about the details of the types of dyssynchrony, diagnosis, course and influence on the progression of CHF. The publication also presents the changes of myocardial synchrony after the improvement of myocardial blood supply as a result of revascularizatio

The definition of specific antiparkinsonian effects of Rapitalam

Previously, we identified a metabotropic glutamate receptor 4 (mGluR4) as a potential target for drugs and predicted that activation of mGluR4 could provide a palliative advantage in the treatment of Parkinson's disease. Determine the mechanism of action of Rapitalam in vitro on a cell culture with mGluR4 over expression. The HEK293T cell line expressing human mGluR4 was used in the wor

A remark on Hamilton cycles with few colors

Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of Kn with n colours contains a Hamilton cycle with ≤O(logn) colours. They proved that there is always a Hamilton cycle with ≤8√n colours. In this note we improve this bound to O(log3n)

Ramsey goodness of bounded degree trees

Given a pair of graphs G and H, the Ramsey number R(G,H) is the smallest N such that every red-blue coloring of the edges of the complete graph KN contains a red copy of G or a blue copy of H. If a graph G is connected, it is well known and easy to show that R(G,H)≥(|G|−1)(χ(H)−1)+σ(H), where χ(H) is the chromatic number of H and σ(H) is the size of the smallest color class in a χ(H)-coloring of H. A graph G is called H-good if R(G,H)=(|G|−1)(χ(H)−1)+σ(H). The notion of Ramsey goodness was introduced by Burr and Erdős in 1983 and has been extensively studied since then. In this paper we show that if n≥Ω(|H|log4|H|) then every n-vertex bounded degree tree T is H-good. The dependency between n and |H| is tight up to log factors. This substantially improves a result of Erdős, Faudree, Rousseau, and Schelp from 1985, who proved that n-vertex bounded degree trees are H-good when when n≥Ω(|H|4)

Experimental approaches to the assessment of potential cardioprotective means with doxorubicin-associated cardiomyopathy

Development of methodological approaches for evaluation of cardioprotective activity of drugs in doxorubicin cardiomyopath

Tissue distribution of potential antidiabetic agent C7070

C7070 is a novel imidazoline receptors agonist for the treatment of diabetes mellitus. The study was included 12 male Wistar rats. The C7070 concentration was determined by highperformance liquid chromatography with tandem mass spectrometry detectio

Effect of magnetic and non-magnetic impurities on highly anisotropic superconductivity

We generalize Abrikosov-Gor'kov solution of the problem of weakly coupled superconductor with impurities on the case of a multiband superconductor with arbitrary interband order parameter anisotropy, including interband sign reversal of the order parameter. The solution is given in terms of the effective (renormalized) coupling matrix and describes not only $T_c$ suppression but also renormalization of the superconducting gap basically at all temperatures. In many limiting cases we find analytical solutions for the critical temperature suppression. We illustrate our results by numerical calculations for two-band model systems.Comment: 18 pages (12pt) RevTeX, 4 postscript figure