2,750 research outputs found
Moodle as a central platform for the Virtual Campus
Moodle als zentrale Plattform für den virtuellen CampusThe Moodle technology served as base for the creation and implementation of the eCampus, a simple system, that integrates all digital services of the school and that, at the same time, gives the professors access to some e-learning resources. Pre-existing digital resources were adapted and combined with new functionalities on top of a Moodle base.
These resources and the context of their use will be presented, as well as some of the necessary technical efforts to implement a useful e-learning platform, while keeping it as easy-to-use as possible. This is why this paper can also described as a hands-on case study of the implementation of a holistic e-learning strategy, with the help of Moodle
The Planar Tree Packing Theorem
Packing graphs is a combinatorial problem where several given graphs are
being mapped into a common host graph such that every edge is used at most
once. In the planar tree packing problem we are given two trees T1 and T2 on n
vertices and have to find a planar graph on n vertices that is the
edge-disjoint union of T1 and T2. A clear exception that must be made is the
star which cannot be packed together with any other tree. But according to a
conjecture of Garc\'ia et al. from 1997 this is the only exception, and all
other pairs of trees admit a planar packing. Previous results addressed various
special cases, such as a tree and a spider tree, a tree and a caterpillar, two
trees of diameter four, two isomorphic trees, and trees of maximum degree
three. Here we settle the conjecture in the affirmative and prove its general
form, thus making it the planar tree packing theorem. The proof is constructive
and provides a polynomial time algorithm to obtain a packing for two given
nonstar trees.Comment: Full version of our SoCG 2016 pape
The number of crossings in multigraphs with no empty lens
Let be a multigraph with vertices and edges, drawn in the
plane such that any two parallel edges form a simple closed curve with at least
one vertex in its interior and at least one vertex in its exterior. Pach and
T\'oth (2018) extended the Crossing Lemma of Ajtai et al. (1982) and Leighton
(1983) by showing that if no two adjacent edges cross and every pair of
nonadjacent edges cross at most once, then the number of edge crossings in
is at least , for a suitable constant . The situation
turns out to be quite different if nonparallel edges are allowed to cross any
number of times. It is proved that in this case the number of crossings in
is at least . The order of magnitude of this bound
cannot be improved.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
On Compact RAC Drawings
We present new bounds for the required area of Right Angle Crossing (RAC) drawings for complete graphs, i.e. drawings where any two crossing edges are perpendicular to each other. First, we improve upon results by Didimo et al. [Walter Didimo et al., 2011] and Di Giacomo et al. [Emilio Di Giacomo et al., 2011] by showing how to compute a RAC drawing with three bends per edge in cubic area. We also show that quadratic area can be achieved when allowing eight bends per edge in general or with three bends per edge for p-partite graphs. As a counterpart, we prove that in general quadratic area is not sufficient for RAC drawings with three bends per edge
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