520 research outputs found
Blocking optimal -arborescences
Given a digraph and a positive integer , an arc set is called a \textbf{-arborescence} if it is the disjoint union of
spanning arborescences. The problem of finding a minimum cost -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 -arborescence. For
, the problem was solved in [A. Bern\'ath, G. Pap , Blocking optimal
arborescences, IPCO 2013]. In this paper we give an algorithm for general
that has polynomial running time if 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 and two "object
types" and chosen from the alternatives above, we
consider the following questions. \textbf{Packing problem:} can we find an
object of type and one of type in the edge set of
, so that they are edge-disjoint? \textbf{Partitioning problem:} can we
partition into an object of type and one of type ?
\textbf{Covering problem:} can we cover with an object of type
, and an object of type ? 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 - path and an - path that are
edge-disjoint. However, many others were not, for example can we find an
- path and a spanning tree 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)
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
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