Embedding graphs having Ore-degree at most five

Let $H$ and $G$ be graphs on $n$ vertices, where $n$ is sufficiently large. We prove that if $H$ has Ore-degree at most 5 and $G$ has minimum degree at least $2n/3$ then $H\subset G.$Comment: accepted for publication at SIAM J. Disc. Mat

On the Advice Complexity of Online Unit Clustering

In online unit clustering a set of n points of a metric space that arrive one by one, partition the points into clusters of diameter at most one, so that number of clusters is minimized. This paper gives linear upper and lower bounds for the advice complexity of 1-competitive online unit clustering algorithms in terms of number of points in $\mathbb{R}^d$ and $\mathbb{Z}^d$

On the advice complexity of coloring bipartite graphs and two-colorable hypergraphs

In the online coloring problem the vertices are revealed one by one to an online algorithm, which has to color them immediately as they appear. The advice complexity attempts to measure how much knowledge of the future is neccessary to achieve a given competitive ratio. Here, we examine coloring of bipartite graphs, proper and the conflict-free coloring of k-uniform hypergraphs and we provide lower and upper bounds for the number of bits of advice to achieve the optimal cost. For bipartite graphs the upper bound n − 2 is tight. For the proper coloring, n − 2k bits are necessary and n − 2 bits are sufficient, while for the conflict-free coloring case n − 2 bits of advice are neccessary and sufficient to color optimally if k > 3

On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity

We give an upper bound of n((n-1)!-(n-3)!) for the possible largest size of a subsemigroup of the full transformational semigroup over n elements consisting only of nonpermutational transformations. As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well

Prevalence Rate of Diabetes Mellitus and Impaired Fasting Glycemia in Hungary: Crosssectional Study on Nationally Representative Sample of People Aged 20-69 Years

Aim To obtain correct evaluation of the prevalence rate of diabetes mellitus and impaired fasting glycemia (IFG) in Hungary. Method The study was performed on a nationally representative sample covered by the Hungarian General Practitioners’ Morbidity Sentinel Stations Program. The source population consisted of all persons aged 20-69 years who were registered with the participating centers. The prevalence rates were adjusted to age and sex distribution of the total Hungarian population. Fasting blood samples of 1803 participants were evaluated. Response rate was 90.7%. Results In addition to 130 (7.21%) patients with established diabetes, 26 participants with newly diagnosed diabetes were found, resulting in a total crude diabetes prevalence of 8.65% (men: 11.16%; women: 6.41%; P < 0.001). After weighting for age and sex, the prevalence rate of diabetes in participants aged 20-69 years should be set at 7.47% (95% confidence interval [CI], 6.26-8.69) (men: 9.49%; 95% CI, 7.52-11.46; women: 5.58%; 95% CI, 4.12-7.04). In addition to 41 (2.27%) patients with established IFG (fasting blood glucose: 6.1-6.9 mmol/L), 47 participants with newly diagnosed IFG were found, resulting in a total crude IFG prevalence of 4.88% (men: 6.11%; women: 3.78%; P = 0.022). After making corrections for weighting age and sex, the total IFG prevalence rate in participants aged 20-69 years should be set at 4.39% (95% CI, 3.44-5.34) (men: 5.52%; 95% CI, 3.99- 7.06; women: 3.33%; 95% CI, 2.19-4.47). Conclusion The prevalence rate of diabetes and IFG in Hungary is higher than previously estimated by experts and authorities. The present data may serve as a base for comparative investigations in the future