Density version of the Ramsey problem and the directed Ramsey problem

We discuss a variant of the Ramsey and the directed Ramsey problem. First, consider a complete graph on $n$ vertices and a two-coloring of the edges such that every edge is colored with at least one color and the number of bicolored edges $|E_{RB}|$ is given. The aim is to find the maximal size $f$ of a monochromatic clique which is guaranteed by such a coloring. Analogously, in the second problem we consider semicomplete digraph on $n$ vertices such that the number of bi-oriented edges $|E_{bi}|$ is given. The aim is to bound the size $F$ of the maximal transitive subtournament that is guaranteed by such a digraph. Applying probabilistic and analytic tools and constructive methods we show that if $|E_{RB}|=|E_{bi}| = p{n\choose 2}$, ($p\in [0,1)$), then $f, F < C_p\log(n)$ where $C_p$ only depend on $p$, while if $m={n \choose 2} - |E_{RB}| <n^{3/2}$ then $f= \Theta (\frac{n^2}{m+n})$. The latter case is strongly connected to Tur\'an-type extremal graph theory.Comment: 17 pages. Further lower bound added in case $|E_{RB}|=|E_{bi}| = p{n\choose 2}

Permutations over cyclic groups

Generalizing a result in the theory of finite fields we prove that, apart from a couple of exceptions that can be classified, for any elements $a_1,...,a_m$ of the cyclic group of order $m$, there is a permutation $\pi$ such that $1a_{\pi(1)}+...+ma_{\pi(m)}=0$

Institutionalization of Regional Policy and the Regional Institution System in Serbia

This study summarizes aspects of Serbian regional policy with special focus on regions and the development of the regional institutions. The study emphasizes the importance of the issue in the Republic of Serbia in 2010, with the ambition to join the European Union. With the enactment of the new Law on Regional Development and the legal framework five NUTS 2 regions were created. The Ministry of Economy and Regional Development is responsible for the institutional coordination of the regional policy. Regional Development Agencies are at the intermediate level of institutional hierarchy. After the regionalization of Serbia, the Autonomous Province of Vojvodina remained a whole and unified NUTS 2 region with complex and developed regional institutions

The Fight against income evasion in Hungary

The evasion of income causes the national budget of Hungary great damage. Just the partial prevention of it would benefit greatly to the state balance and the realization of the economic policy in Hungary. Repelling income evasion can only be achieved by various means. These are the following: To identify and abolish its reasons and causes; to post strict regularizations consistent with the EU legislation; to close legal gaps; not to concentrate on penalties; to reduce high taxes and the exorbitant income centralization of the state; to take the moral education for serious as well as the legal harmonization and effect analysis for the various decisions.

On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method

We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $F\subseteq \binom{[n]}{k}$. Improving a bound of Balogh at al. on $M(n,k)$, we determine the order of magnitude of $\log M(n,k)$ by proving that for any fixed $k$, $M(n,k) =n^{\Theta(\binom{2k}{k})}$ holds. Our proof is based on Tuza's set pair approach. The main idea is to bound the size of the largest possible point set of a cross-intersecting system. We also introduce and investigate some related functions and parameters.Comment: 11 page