Blocking optimal kk-arborescences

Given a digraph $D=(V,A)$ and a positive integer $k$, an arc set $F\subseteq A$ is called a \textbf{$k$-arborescence} if it is the disjoint union of $k$ spanning arborescences. The problem of finding a minimum cost $k$-arborescence is known to be polynomial-time solvable using matroid intersection. In this paper we study the following problem: find a minimum cardinality subset of arcs that contains at least one arc from every minimum cost $k$-arborescence. For $k=1$, the problem was solved in [A. Bern\'ath, G. Pap , Blocking optimal arborescences, IPCO 2013]. In this paper we give an algorithm for general $k$ that has polynomial running time if $k$ is fixed

On the tractability of some natural packing, covering and partitioning problems

In this paper we fix 7 types of undirected graphs: paths, paths with prescribed endvertices, circuits, forests, spanning trees, (not necessarily spanning) trees and cuts. Given an undirected graph $G=(V,E)$ and two "object types" $\mathrm{A}$ and $\mathrm{B}$ chosen from the alternatives above, we consider the following questions. \textbf{Packing problem:} can we find an object of type $\mathrm{A}$ and one of type $\mathrm{B}$ in the edge set $E$ of $G$, so that they are edge-disjoint? \textbf{Partitioning problem:} can we partition $E$ into an object of type $\mathrm{A}$ and one of type $\mathrm{B}$? \textbf{Covering problem:} can we cover $E$ with an object of type $\mathrm{A}$, and an object of type $\mathrm{B}$? This framework includes 44 natural graph theoretic questions. Some of these problems were well-known before, for example covering the edge-set of a graph with two spanning trees, or finding an $s$-$t$ path $P$ and an $s'$-$t'$ path $P'$ that are edge-disjoint. However, many others were not, for example can we find an $s$-$t$ path $P\subseteq E$ and a spanning tree $T\subseteq E$ that are edge-disjoint? Most of these previously unknown problems turned out to be NP-complete, many of them even in planar graphs. This paper determines the status of these 44 problems. For the NP-complete problems we also investigate the planar version, for the polynomial problems we consider the matroidal generalization (wherever this makes sense)

Characterization of the Plasma Shape of the TIG Welding Arc

Tungsten electrodes were prepared to analyse the plasma geometry at TIG welding. The investigated electrodes were La02, Th02 alloyed. Tip flatted electrodes were grinded as well. The shape of plasma were analysed for 36 different electrodes. Analysing of digital pictures, the plasma geometry were measured. Whole and brightest plasma area was checked as well. Measured values were represented as a function of taper angles. Main conclusion is that the maximum of the diagrams, which characterise the effect of taper angle for sharpened electrodes, were at taper angle of 20-30°. The properties of the red and the black electrodes are running collaterally. Despite of them the characteristics of the gold electrode shift to higher taper angles causing by the high La02 content of the electrode. There was no clear correlation between the electrode taper angle and the shape characteristics of plasma for the electrodes, which were prepared with a flat tip

Investigation of TIG-welding plasma and the electrode contamination

TIG welding experiments have been used for the welded joints of the austenitic stainless steel and molybdenum. The aim of the experiments was to find the optimal welding parameters. The problems that occurred throughout the welding process were due to the very high melting point of the Mo. Also, using optical microscopy and scanning electron microscopy have performed a proper testing in parallel with the experiments. Regarding to the wear of electrode, there have been determined the tip angle, the tapering and the effect of the electrode’s material composition. The latter parameter was investigated for thorium-oxide and lanthanum-oxide alloyed electrodes