107,974 research outputs found
Layout of Graphs with Bounded Tree-Width
A \emph{queue layout} of a graph consists of a total order of the vertices,
and a partition of the edges into \emph{queues}, such that no two edges in the
same queue are nested. The minimum number of queues in a queue layout of a
graph is its \emph{queue-number}. A \emph{three-dimensional (straight-line
grid) drawing} of a graph represents the vertices by points in
and the edges by non-crossing line-segments. This paper contributes three main
results:
(1) It is proved that the minimum volume of a certain type of
three-dimensional drawing of a graph is closely related to the queue-number
of . In particular, if is an -vertex member of a proper minor-closed
family of graphs (such as a planar graph), then has a drawing if and only if has O(1) queue-number.
(2) It is proved that queue-number is bounded by tree-width, thus resolving
an open problem due to Ganley and Heath (2001), and disproving a conjecture of
Pemmaraju (1992). This result provides renewed hope for the positive resolution
of a number of open problems in the theory of queue layouts.
(3) It is proved that graphs of bounded tree-width have three-dimensional
drawings with O(n) volume. This is the most general family of graphs known to
admit three-dimensional drawings with O(n) volume.
The proofs depend upon our results regarding \emph{track layouts} and
\emph{tree-partitions} of graphs, which may be of independent interest.Comment: This is a revised version of a journal paper submitted in October
2002. This paper incorporates the following conference papers: (1) Dujmovic',
Morin & Wood. Path-width and three-dimensional straight-line grid drawings of
graphs (GD'02), LNCS 2528:42-53, Springer, 2002. (2) Wood. Queue layouts,
tree-width, and three-dimensional graph drawing (FSTTCS'02), LNCS
2556:348--359, Springer, 2002. (3) Dujmovic' & Wood. Tree-partitions of
-trees with applications in graph layout (WG '03), LNCS 2880:205-217, 200
Roughness Signature of Tribological Contact Calculated by a New Method of Peaks Curvature Radius Estimation on Fractal Surfaces
This paper proposes a new method of roughness peaks curvature radii calculation and its application to tribological contact analysis as characteristic signature of tribological contact. This method is introduced via the classical approach of the calculation of radius of asperity. In fact, the proposed approach provides a generalization to fractal profiles of the Nowicki's method [Nowicki B. Wear Vol.102, p.161-176, 1985] by introducing a fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the studied profile. It is then established the increasing of the dispersion of the measures of that lines with that of the corresponding radii and the dependence of calculated radii on the fractal dimension of the studied curve. Consequently, the notion of peak is mathematically reformulated. The efficiency of the proposed method was tested via simulations of fractal curves such as those described by Brownian motions. A new fractal function allowing the modelling of a large number of physical phenomena was also introduced, and one of the great applications developed in this paper consists in detecting the scale on which the measurement system introduces a smoothing artifact on the data measurement. New methodology is applied to analysis of tribological contact in metal forming process
The Orchard crossing number of an abstract graph
We introduce the Orchard crossing number, which is defined in a similar way
to the well-known rectilinear crossing number. We compute the Orchard crossing
number for some simple families of graphs. We also prove some properties of
this crossing number.
Moreover, we define a variant of this crossing number which is tightly
connected to the rectilinear crossing number, and compute it for some simple
families of graphs.Comment: 17 pages, 10 figures. Totally revised, new material added. Submitte
JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes
A new version of the Feynman graph plotting tool JaxoDraw is presented.
Version 2.0 is a fundamental re-write of most of the JaxoDraw core and some
functionalities, in particular importing graphs, are not backward-compatible
with the 1.x branch. The most prominent new features include: drawing of Bezier
curves for all particle modes, on-the-fly update of edited objects, multiple
undo/redo functionality, the addition of a plugin infrastructure, and a general
improved memory performance. A new LaTeX style file is presented that has been
written specifically on top of the original axodraw.sty to meet the needs of
this this new version.Comment: 17 pages, 1 figur
3D Visibility Representations of 1-planar Graphs
We prove that every 1-planar graph G has a z-parallel visibility
representation, i.e., a 3D visibility representation in which the vertices are
isothetic disjoint rectangles parallel to the xy-plane, and the edges are
unobstructed z-parallel visibilities between pairs of rectangles. In addition,
the constructed representation is such that there is a plane that intersects
all the rectangles, and this intersection defines a bar 1-visibility
representation of G.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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