394 research outputs found
Approximately coloring graphs without long induced paths
It is an open problem whether the 3-coloring problem can be solved in
polynomial time in the class of graphs that do not contain an induced path on
vertices, for fixed . We propose an algorithm that, given a 3-colorable
graph without an induced path on vertices, computes a coloring with
many colors. If the input graph is
triangle-free, we only need many
colors. The running time of our algorithm is if the input
graph has vertices and edges
Magnetic domain-wall motion by propagating spin waves
We found by micromagnetic simulations that the motion of a transverse wall
(TW) type domain wall in magnetic thin-film nanostripes can be manipulated via
interaction with spin waves (SWs) propagating through the TW. The velocity of
the TW motion can be controlled by changes of the frequency and amplitude of
the propagating SWs. Moreover, the TW motion is efficiently driven by specific
SW frequencies that coincide with the resonant frequencies of the local modes
existing inside the TW structure. The use of propagating SWs, whose frequencies
are tuned to those of the intrinsic TW modes, is an alternative approach for
controlling TW motion in nanostripes
Pennsylvanian-Early Triassic stratigraphy in the Alborz Mountains (Iran)
New fieldwork was carried out in the central and eastern Alborz, addressing the sedimentary succession from the Pennsylvanian to the Early Triassic. A regional synthesis is proposed, based on sedimentary analysis and a wide collection of new palaeontological data. The Moscovian Qezelqaleh Formation, deposited in a mixed coastal marine and alluvial setting, is present in a restricted area of the eastern Alborz, transgressing on the Lower Carboniferous Mobarak and Dozdehband formations. The late Gzhelianâearly Sakmarian Dorud Group is instead distributed over most of the studied area, being absent only in a narrow belt to the SE. The Dorud Group is typically tripartite, with a terrigenous unit in the lower part (Toyeh Formation), a carbonate intermediate part (Emarat and Ghosnavi formations, the former particularly rich in fusulinids), and a terrigenous upper unit (Shah Zeid Formation), which however seems to be confined to the central Alborz. A major gap in sedimentation occurred before the deposition of the overlying Ruteh Limestone, a thick package of packstoneâwackestone interpreted as a carbonate ramp of Middle Permian age (WordianâCapitanian). The Ruteh Limestone is absent in the eastern part of the range, and everywhere ends with an emersion surface, that may be karstified or covered by a lateritic soil.
The Late Permian transgression was directed southwards in the central Alborz, where marine facies (Nesen Formation) are more common. Time-equivalent alluvial fans with marsh intercalations and lateritic soils (Qeshlaq Formation) are present in the east. Towards the end of the Permian most of the Alborz emerged, the marine facies being restricted to a small area on the Caspian side of the central Alborz. There, the Permo-Triassic boundary interval is somewhat similar to the AbadehâShahreza belt in central Iran, and contains oolites, flat microbialites and domal stromatolites, forming the base of the Elikah Formation. The PâT boundary is established on the basis of conodonts, small foraminifera and stable isotope data. The development of the lower and middle part of the Elikah Formation, still Early Triassic in age, contains vermicular bioturbated mudstone/wackestone, and anachronostic-facies-like gastropod oolites and flat pebble conglomerates.
Three major factors control the sedimentary evolution. The succession is in phase with global sea-level curve in the Moscovian and from the Middle Permian upwards. It is out of phase around the CarboniferousâPermian boundary, when the Dorud Group was deposited during a global lowstand of sealevel. When the global deglaciation started in the Sakmarian, sedimentation stopped in the Alborz and the area emerged. Therefore, there is a consistent geodynamic control. From the Middle Permian upwards, passive margin conditions control the sedimentary evolution of the basin, which had its depocentre(s) to the north. Climate also had a significant role, as the Alborz drifted quickly northwards with other central Iran blocks towards the Turan active margin. It passed from a southern latitude through the aridity belt in the Middle Permian, across the equatorial humid belt in the Late Permian and reached the northern arid tropical belt in the Triassic
Complexity of Coloring Graphs without Paths and Cycles
Let and denote a path on vertices and a cycle on
vertices, respectively. In this paper we study the -coloring problem for
-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada,
have proved that 3-colorability of -free graphs has a finite forbidden
induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and
Vatshelle have shown that -colorability of -free graphs for
does not. These authors have also shown, aided by a computer search, that
4-colorability of -free graphs does have a finite forbidden induced
subgraph characterization. We prove that for any , the -colorability of
-free graphs has a finite forbidden induced subgraph
characterization. We provide the full lists of forbidden induced subgraphs for
and . As an application, we obtain certifying polynomial time
algorithms for 3-coloring and 4-coloring -free graphs. (Polynomial
time algorithms have been previously obtained by Golovach, Paulusma, and Song,
but those algorithms are not certifying); To complement these results we show
that in most other cases the -coloring problem for -free
graphs is NP-complete. Specifically, for we show that -coloring is
NP-complete for -free graphs when and ; for we show that -coloring is NP-complete for -free graphs
when , ; and additionally, for , we show that
-coloring is also NP-complete for -free graphs if and
. This is the first systematic study of the complexity of the
-coloring problem for -free graphs. We almost completely
classify the complexity for the cases when , and
identify the last three open cases
Exhaustive generation of -critical -free graphs
We describe an algorithm for generating all -critical -free
graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove
that there are only finitely many -critical -free graphs, for
both and . We also show that there are only finitely many
-critical graphs -free graphs. For each case of these cases we
also give the complete lists of critical graphs and vertex-critical graphs.
These results generalize previous work by Hell and Huang, and yield certifying
algorithms for the -colorability problem in the respective classes.
Moreover, we prove that for every , the class of 4-critical planar
-free graphs is finite. We also determine all 27 4-critical planar
-free graphs.
We also prove that every -free graph of girth at least five is
3-colorable, and determine the smallest 4-chromatic -free graph of
girth five. Moreover, we show that every -free graph of girth at least
six and every -free graph of girth at least seven is 3-colorable. This
strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with
arXiv:1504.0697
Direct observation of domain wall structures in curved permalloy wires containing an antinotch
The formation and field response of head-to-head domain walls in curved permalloy wires, fabricated to contain a single antinotch, have been investigated using Lorentz microscopy. High spatial resolution maps of the vector induction distribution in domain walls close to the antinotch have been derived and compared with micromagnetic simulations. In wires of 10 nm thickness the walls are typically of a modified asymmetric transverse wall type. Their response to applied fields tangential to the wire at the antinotch location was studied. The way the wall structure changes depends on whether the field moves the wall away from or further into the notch. Higher fields are needed and much more distorted wall structures are observed in the latter case, indicating that the antinotch acts as an energy barrier for the domain wal
List coloring in the absence of a linear forest.
The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)â{1,âŠ,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of HoĂ ng, KamiĆski, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H
On the computation of zone and double zone diagrams
Classical objects in computational geometry are defined by explicit
relations. Several years ago the pioneering works of T. Asano, J. Matousek and
T. Tokuyama introduced "implicit computational geometry", in which the
geometric objects are defined by implicit relations involving sets. An
important member in this family is called "a zone diagram". The implicit nature
of zone diagrams implies, as already observed in the original works, that their
computation is a challenging task. In a continuous setting this task has been
addressed (briefly) only by these authors in the Euclidean plane with point
sites. We discuss the possibility to compute zone diagrams in a wide class of
spaces and also shed new light on their computation in the original setting.
The class of spaces, which is introduced here, includes, in particular,
Euclidean spheres and finite dimensional strictly convex normed spaces. Sites
of a general form are allowed and it is shown that a generalization of the
iterative method suggested by Asano, Matousek and Tokuyama converges to a
double zone diagram, another implicit geometric object whose existence is known
in general. Occasionally a zone diagram can be obtained from this procedure.
The actual (approximate) computation of the iterations is based on a simple
algorithm which enables the approximate computation of Voronoi diagrams in a
general setting. Our analysis also yields a few byproducts of independent
interest, such as certain topological properties of Voronoi cells (e.g., that
in the considered setting their boundaries cannot be "fat").Comment: Very slight improvements (mainly correction of a few typos); add DOI;
Ref [51] points to a freely available computer application which implements
the algorithms; to appear in Discrete & Computational Geometry (available
online
Domain wall propagation in Permalloy nanowires with a thickness gradient
The domain wall nucleation and motion processes in Permalloy nanowires with a
thickness gradient along the nanowire axis have been studied. Nanowires with
widths, w = 250 nm to 3 um and a base thickness of t = 10 nm were fabricated by
electron-beam lithography. The magnetization hysteresis loops measured on
individual nanowires are compared to corresponding nanowires without a
thickness gradient. The Hc vs. t/w curves of wires with and without a thickness
gradient are discussed and compared to micromagnetic simulations. We find a
metastability regime at values of w, where a transformation from transverse to
vortex domain wall type is expected
Parameterized Complexity of Maximum Edge Colorable Subgraph
A graph is {\em -edge colorable} if there is a coloring , such that for distinct , we have
. The {\sc Maximum Edge-Colorable Subgraph} problem
takes as input a graph and integers and , and the objective is to
find a subgraph of and a -edge-coloring of , such that . We study the above problem from the viewpoint of Parameterized
Complexity. We obtain \FPT\ algorithms when parameterized by: the vertex
cover number of , by using {\sc Integer Linear Programming}, and ,
a randomized algorithm via a reduction to \textsc{Rainbow Matching}, and a
deterministic algorithm by using color coding, and divide and color. With
respect to the parameters , where is one of the following: the
solution size, , the vertex cover number of , and l -
{\mm}(G), where {\mm}(G) is the size of a maximum matching in ; we show
that the (decision version of the) problem admits a kernel with vertices. Furthermore, we show that there is no kernel of size
, for any and computable
function , unless \NP \subseteq \CONPpoly
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