The complexity of recognizing minimally tough graphs

A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough. A graph is minimally $t$-tough if the toughness of the graph is $t$ and the deletion of any edge from the graph decreases the toughness. The complexity class DP is the set of all languages that can be expressed as the intersection of a language in NP and a language in coNP. In this paper, we prove that recognizing minimally $t$-tough graphs is DP-complete for any positive rational number $t$. We introduce a new notion called weighted toughness, which has a key role in our proof

Properties of minimally tt-tough graphs

A graph $G$ is minimally $t$-tough if the toughness of $G$ is $t$ and the deletion of any edge from $G$ decreases the toughness. Kriesell conjectured that for every minimally $1$-tough graph the minimum degree $\delta(G)=2$. We show that in every minimally $1$-tough graph $\delta(G)\le\frac{n+2}{3}$. We also prove that every minimally $1$-tough claw-free graph is a cycle. On the other hand, we show that for every $t \in \mathbb{Q}$ any graph can be embedded as an induced subgraph into a minimally $t$-tough graph

Poisson limit of an inhomogeneous nearly critical INAR(1) model

An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound Poisson distribution.Comment: Latex2e pdfeTex Version 3, 22 pages, submitted to ACTA Sci. Math. (Szeged

The Transformation of Hungarian Production Cooperatives and Future Consequences

This research examines the transformation of Hungarian agricultural production cooperatives. In contrast to early expectations, cooperatives did not experience much membership loss. Rather, the enterprises held together, although they downsized. The distribution of collective assets occurred quickly and created much tension. The sector experienced a severe decapitalization, and the efficiency of the sector fell. There was a sharp rise in unemployment. Sales and marketing were disrupted. Thus, the cooperatives transformed in a very hostile situation. They survived, and some prospered, yet, in general, they remain vulnerable to adverse economic developments. Healthy cooperatives will be vital to the success of smaller private farms.Agribusiness,

Nanoelektronikai kvantum-eszközök tér-idő dinamikájának szimulációja a környezeti hatások figyelembevételével = Space-time dynamic simulation of nano-electronic devices considering the effect of the environment

A kutatás keretein belül a kutatási tervnek megfelelően nano-elektronikai eszközök szimulációja történt meg a hagyományos irányvonalnak tekinthető MOS alapú tranzisztorok, és az új architektúrák egyikét képviselő kvantum-pont sejt automata (QCA) esetén. A QCA-t érintő kutatásaink során modelleztük magát a kvantum sejtet a lehetséges kvantummechanikai időfüggő és időfüggetlen állapotok meghatározásával. Vizsgáltuk a környezeti hőmérséklet hatását a kvantummechanikai elektron állapotokra, valamint a vezérlő tér kapcsolási idejét az egyes állapotokra. Programot készítettünk logikai kapuk modellezésére. Elemeztük a szobahőmérsékleten működő QCA megvalósíthatóságának feltételeit, valamint a technológiai realizálás lehetőségeit. A MOS alapú tranzisztorok vizsgálata során kidolgoztunk 1D és 2D megoldó programot a drift diffúziós és sűrűség gradiens modellre. Megvizsgáltuk a modellek érvényességi körét csökkenő oxid vastagság függvényében. Az elektron eloszlás és kapacitás meghatározásával kvantitatív értékeket kaptunk a kvantum effektus lényeges szerepére. Ezenkívül, ekvivalens áramköri szimulációval kimutattuk, hogy a nemlineáris távvezeték esetén a kvantum hatások jelentős viselkedésbeli eltérést eredményezhetnek. | Based on the research plan, nano-electronic devices have been simulated, namely MOS type transistors and Quantum-dot Cellular Automata (QCA). MOS type transistor represents the traditional architecture, however QCA is a new paradigm of computational. In the case of QCA research the quantum cell has been modeled determining the quantum mechanical time dependent and time independent states. We investigated the effect of environmental temperature on electron states and the switching time between the electron states as a function control field. We prepared a computational program to simulate the logical gates. Realization of QCA on room temperature has been analyzed in the aspect of physical conditions and technological view point. During the research of MOS type transistors we developed 1D and 2D software in case of drift diffusion and density gradient model. The scope of the models has been investigated as a function of oxide thickness. Determining the electron density and capacitance we got quantitative description of significant quantum effects. On the other hand, using equivalent circuit simulation we pointed out the quantum effect - in the case of non-linear transmission line - could cause remarkable distortion