Edge-connectivity augmentation of graphs over symmetric parity families

AbstractIn this note we solve the edge-connectivity augmentation problem over symmetric parity families. It provides a solution for the minimum T-cut augmentation problem. We also extend a recent result of Zhang [C.Q. Zhang, Circular flows of nearly eulerian graphs and vertex splitting, J. Graph Theory 40 (2002) 147–161]

Mechanism of paraquat resistance – from the antioxidant enzymes to the transporters

In this paper a review of the most important results on the paraquat resistance mechanism of weeds is given, with special respect on horseweed Conyza canadensis (L.) Cronq. There is no difference between susceptible and resistant plants in the activity of antioxidant enzymes and in the penetration of paraquat into the chloroplasts. The paraquat resistance is primarily based on higher expression of a putative amino acid/polyamine transporter which is responsible for the exclusion of paraquat into the vacuole in resistant horseweed

On a min–max theorem on bipartite graphs

AbstractFrank et al. (Math. Programming Stud. 22 (1984) 99–112) proved that for any connected bipartite graft (G,T), the minimum size of a T-join is equal to the maximum value of a partition of A, where A is one of the two colour classes of G. Their proof consists of constructing a partition of A of value |F|, by using a minimum T-join F. That proof depends heavily on the properties of distances in graphs with conservative weightings. We follow the dual approach, that is starting from a partition of A of maximum value k, we construct a T-join of size k. Our proof relies only on Tutte's theorem on perfect matchings. It is known (J. Combin. Theory Ser. B 61 (2) (1994) 263–271) that the results of Lovász on 2-packing of T-cuts, of Seymour on packing of T-cuts in bipartite graphs and in grafts that cannot be T-contracted onto (K4,V(K4)), and of Sebő on packing of T-borders are implied by this theorem of Frank et al. The main contribution of the present paper is that all of these results can be derived from Tutte's theorem

Protestáns kisegyházak a 20. századi magyar társadalomban = Free Churches in Hungarian Society in the 20th Century

A pályázatban vállalt feladatainkat teljesítettük. Egy tankönyvnek is alkalmas kettősmonográfiával (Rajki Zoltán – Szigeti Jenő: Szabadegyházak története Magyarországon 1989-ig, Budapest, 2012, Gondolat) először tártuk fel a magyarországi szabadegyházak 1989 előtti történetét. Ezen kívül elkészült két monográfia egy-egy szabadegyházi közösség történetének egy-egy szakaszáról (Rajki Zoltán: A pünkösdi mozgalom története Magyarországon 1945 és 1961 között, Budapest, Gondolat, 2011; Rajki Zoltán: Az Egervári-mozgalom. A Keresztény Advent Közösség kialakulása és vallásszabadsági küzdelmei a Kádár-korszak második felében 1975-1990, Budapest, 2012, Gondolat). A 2011. májusi konferencia írásos anyaga megjelenés előtt áll a Gondolat Kiadónál. A fentieken kívül elkészítettünk egy online tanulmánykötetet. Több konferencián témával kapcsolatos előadásokat tartottunk. A fent említett könyveken, szerkesztett köteteken kívül 5 könyvfejezetet, 12 folyóiratcikket, 6 konferenciacikket publikáltunk az OTKA támogatásának feltüntetésével. Összeállítottunk egy tudományos weblapot (www.kisegyhazkutato.hu), amelyen számos forrást, folyóiratanyagot és 180 szabadegyházakra vonatkozó térképet tettünk közzé, hogy mások kutatómunkáját segítsük. | We have fulfilled all the OTKA grant expectations of the “Small Protestant Churches in the 20th Century Hungarian Society”. We finished and published the book: The History of the Hungarian Free Churches Before 1989 (Budapest, 2012, Gondolat) that is also suitable as a university textbook. In addition to this book, I also have published two monographs about different periods of the Seventh-day Adventist Church and the Pentecostal movement. (Rajki, Z.: A pünkösdi mozgalom története Magyarországon 1945 és 1961 között, Budapest, Gondolat, 2011; and Rajki, Z.: Az Egervári-mozgalom. A Keresztény Advent Közösség kialakulása és vallásszabadsági küzdelmei a Kádár-korszak második felében 1975-1990, Budapest, 2012, Gondolat). The written version of the “Free Churches, Religious Minorities and the Dictatorship in Europe in the 20th Centuries” conference held in May of 2011 will be published by the Gondolat Publishing House at the end of 2012. Furthermore, Jenő Szigeti and I have published a volume of studies in online form and we also gave presentations about our research topics in several conferences. Aside from the above mentioned books, we have published 5 book chapters and 13 articles in different journals and 5 conference papers which were supported by OTKA. We also have compiled a scholarly website (www.kisegyhazkutato.hu), with numerous sources, journals, and 180 maps about the Free Churches and made it available for free public use

XILINX BASED HARDWARE FOR PICTURE PROCESSING AND CHARACTER RECOGNITION PURPOSES

The paper deals with the development of hardware that is capable realising picture pro- cessing and character recognition algorithms. The hardware was implemented as an IBM PC peripheral card and contains up to five XILINX XC 3090 FPGA devices. Because of the on board reconfigurability of the XILINX devices the hardware allows to imple- ment several separate algorithms at different times. For evaluation the performance of the hardware the Dineen and the linger image smoothing techniques were chosen. The image smoothing techniques can be used at the pre-processing stage of the character recognition process

The (2,k)(2,k)-connectivity augmentation problem: Algorithmic aspects

Durand de Gevigney and Szigeti \cite{DgGSz} have recently given a min-max theorem for the $(2,k)$-connectivity augmentation problem. This article provides an $O(n^3(m+ n \textrm{ }log\textrm{ }n))$ algorithm to find an optimal solution for this problem

Steiner connectivity problems in hypergraphs

We say that a tree $T$ is an $S$-Steiner tree if $S \subseteq V(T)$ and a hypergraph is an $S$-Steiner hypertree if it can be trimmed to an $S$-Steiner tree. We prove that it is NP-hard to decide, given a hypergraph $\mathcal{H}$ and some $S \subseteq V(\mathcal{H})$, whether there is a subhypergraph of $\mathcal{H}$ which is an $S$-Steiner hypertree. As corollaries, we give two negative results for two Steiner orientation problems in hypergraphs. Firstly, we show that it is NP-hard to decide, given a hypergraph $\mathcal{H}$, some $r \in V(\mathcal{H})$ and some $S \subseteq V(\mathcal{H})$, whether this hypergraph has an orientation in which every vertex of $S$ is reachable from $r$. Secondly, we show that it is NP-hard to decide, given a hypergraph $\mathcal{H}$ and some $S \subseteq V(\mathcal{H})$, whether this hypergraph has an orientation in which any two vertices in $S$ are mutually reachable from each other. This answers a longstanding open question of the Egerv\'ary Research group. On the positive side, we show that the problem of finding a Steiner hypertree and the first orientation problem can be solved in polynomial time if the number of terminals $|S|$ is fixed

Packing of mixed hyperarborescences with flexible roots via matroid intersection

Given a mixed hypergraph $\mathcal{F}=(V,\mathcal{A}\cup \mathcal{E})$, functions $f,g:V\rightarrow \mathbb{Z}_+$ and an integer $k$, a packing of $k$ spanning mixed hyperarborescences is called $(k,f,g)$-flexible if every $v \in V$ is the root of at least $f(v)$ and at most $g(v)$ of the mixed hyperarborescences. We give a characterization of the mixed hypergraphs admitting such packings. This generalizes results of Frank and, more recently, Gao and Yang. Our approach is based on matroid intersection, generalizing a construction of Edmonds. We also obtain an algorithm for finding a minimum weight solution to the above mentioned problem

On reversing arcs to improve arc-connectivity

We show that if the arc-connectivity of a directed graph $D$ is at most $\lfloor\frac{k+1}{2}\rfloor$ and the reorientation of an arc set $F$ in $D$ results in a $k$-arc-connected directed graph then we can reorient one arc of $F$ without decreasing the arc-connectivity of $D.$ This improves a result of Fukuda, Prodon, Sakuma and one of Ito et al. for $k\in\{2,3\}$.Comment: 8 page