3,791 research outputs found
Identification of the byproducts of the oxygen evolution reaction on rutile-type oxides under dynamic conditions
Peer reviewedPostprin
Structural parameterizations for boxicity
The boxicity of a graph is the least integer such that has an
intersection model of axis-aligned -dimensional boxes. Boxicity, the problem
of deciding whether a given graph has boxicity at most , is NP-complete
for every fixed . We show that boxicity is fixed-parameter tractable
when parameterized by the cluster vertex deletion number of the input graph.
This generalizes the result of Adiga et al., that boxicity is fixed-parameter
tractable in the vertex cover number.
Moreover, we show that boxicity admits an additive -approximation when
parameterized by the pathwidth of the input graph.
Finally, we provide evidence in favor of a conjecture of Adiga et al. that
boxicity remains NP-complete when parameterized by the treewidth.Comment: 19 page
On a Tree and a Path with no Geometric Simultaneous Embedding
Two graphs and admit a geometric simultaneous
embedding if there exists a set of points P and a bijection M: P -> V that
induce planar straight-line embeddings both for and for . While it
is known that two caterpillars always admit a geometric simultaneous embedding
and that two trees not always admit one, the question about a tree and a path
is still open and is often regarded as the most prominent open problem in this
area. We answer this question in the negative by providing a counterexample.
Additionally, since the counterexample uses disjoint edge sets for the two
graphs, we also negatively answer another open question, that is, whether it is
possible to simultaneously embed two edge-disjoint trees. As a final result, we
study the same problem when some constraints on the tree are imposed. Namely,
we show that a tree of depth 2 and a path always admit a geometric simultaneous
embedding. In fact, such a strong constraint is not so far from closing the gap
with the instances not admitting any solution, as the tree used in our
counterexample has depth 4.Comment: 42 pages, 33 figure
Contact Representations of Graphs in 3D
We study contact representations of graphs in which vertices are represented
by axis-aligned polyhedra in 3D and edges are realized by non-zero area common
boundaries between corresponding polyhedra. We show that for every 3-connected
planar graph, there exists a simultaneous representation of the graph and its
dual with 3D boxes. We give a linear-time algorithm for constructing such a
representation. This result extends the existing primal-dual contact
representations of planar graphs in 2D using circles and triangles. While
contact graphs in 2D directly correspond to planar graphs, we next study
representations of non-planar graphs in 3D. In particular we consider
representations of optimal 1-planar graphs. A graph is 1-planar if there exists
a drawing in the plane where each edge is crossed at most once, and an optimal
n-vertex 1-planar graph has the maximum (4n - 8) number of edges. We describe a
linear-time algorithm for representing optimal 1-planar graphs without
separating 4-cycles with 3D boxes. However, not every optimal 1-planar graph
admits a representation with boxes. Hence, we consider contact representations
with the next simplest axis-aligned 3D object, L-shaped polyhedra. We provide a
quadratic-time algorithm for representing optimal 1-planar graph with L-shaped
polyhedra
Long-Term Alendronate Use Not without Consequences?
A previously unknown side effect of biphosphonate use is emerging. In a specific patient group on long term biphosphonate therapy stress femur fractures seem to occur. The typical presentation consists of prodromal pain in the affected leg and/or a discrete cortical thickening on the lateral side of the femur in conventional radiological examination or the presentation with a spontaneous transverse subtrochanteric femur with typical features. We present three cases of this stress fracture in patients on bisphosphonate therapy. One of these patients suffered a bilateral femur fracture of the same type. In our opinion, in patients on bisphosphonate therapy who present with a spontaneous femur fracture, seizing therapy is advisable. In bilateral cases preventive nailing should be considered
Crystallographic structure of ultrathin Fe films on Cu(100)
We report bcc-like crystal structures in 2-4 ML Fe films grown on fcc Cu(100)
using scanning tunneling microscopy. The local bcc structure provides a
straightforward explanation for their frequently reported outstanding magnetic
properties, i.e., ferromagnetic ordering in all layers with a Curie temperature
above 300 K. The non-pseudomorphic structure, which becomes pseudomorphic above
4 ML film thickness is unexpected in terms of conventional rules of thin film
growth and stresses the importance of finite thickness effects in ferromagnetic
ultrathin films.Comment: 4 pages, 3 figures, RevTeX/LaTeX2.0
Plasmas and Controlled Nuclear Fusion
Contains reports on three research projects.U. S. Atomic Energy Commission (Contract AT(30-1)-3980
Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count
We show that triangle-free penny graphs have degeneracy at most two, list
coloring number (choosability) at most three, diameter , and
at most edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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