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Related papers: Upward planar drawings with two slopes

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We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The…

Computational Geometry · Computer Science 2026-05-04 Patrizio Angelini , Sabine Cornelsen , Giordano Da Lozzo , Fabrizio Frati , Philipp Kindermann , Ignaz Rutter , Johannes Zink

In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface S of genus g and produce a planar drawing of G in R^2, with a bounding face defined by a polygonal…

Computational Geometry · Computer Science 2009-08-13 Christian A. Duncan , Michael T. Goodrich , Stephen G. Kobourov

It is proved that every series-parallel digraph whose maximum vertex-degree is $\Delta$ admits an upward planar drawing with at most one bend per edge such that each edge segment has one of $\Delta$ distinct slopes. This is shown to be…

Computational Geometry · Computer Science 2016-08-31 Emilio Di Giacomo , Giuseppe Liotta , Fabrizio Montecchiani

We introduce and study level-planar straight-line drawings with a fixed number $\lambda$ of slopes. For proper level graphs, we give an $O(n \log^2 n / \log \log n)$-time algorithm that either finds such a drawing or determines that no such…

Data Structures and Algorithms · Computer Science 2019-08-02 Guido Brückner , Nadine Davina Krisam , Tamara Mchedlidze

The slope number of a graph $G$ is the smallest number of slopes needed for the segments representing the edges in any straight-line drawing of $G$. It serves as a measure of the visual complexity of a graph drawing. Several bounds on the…

Computational Geometry · Computer Science 2022-10-13 Jonathan Klawitter , Johannes Zink

We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem---to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph---and…

Computational Geometry · Computer Science 2014-10-31 Timothy M. Chan , Fabrizio Frati , Carsten Gutwenger , Anna Lubiw , Petra Mutzel , Marcus Schaefer

We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…

Computational Geometry · Computer Science 2012-06-05 Taylor Gordon

While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…

Point-set embeddings and large-angle crossings are two areas of graph drawing that independently have received a lot of attention in the past few years. In this paper, we consider problems in the intersection of these two areas. Given the…

Data Structures and Algorithms · Computer Science 2011-07-26 Martin Fink , Jan-Henrik Haunert , Tamara Mchedlidze , Joachim Spoerhase , Alexander Wolff

In a planar L-drawing of a directed graph (digraph) each edge e is represented as a polyline composed of a vertical segment starting at the tail of e and a horizontal segment ending at the head of e. Distinct edges may overlap, but not…

Computational Geometry · Computer Science 2020-08-19 Patrizio Angelini , Steven Chaplick , Sabine Cornelsen , Giordano Da Lozzo

We prove that every set $\mathcal S$ of $\Delta$ slopes containing the horizontal slope is universal for $1$-bend upward planar drawings of bitonic $st$-graphs with maximum vertex degree $\Delta$, i.e., every such digraph admits a $1$-bend…

Computational Geometry · Computer Science 2018-08-30 Michael A. Bekos , Emilio Di Giacomo , Walter Didimo , Giuseppe Liotta , Fabrizio Montecchiani

We present an algorithm to support the dynamic embedding in the plane of a dynamic graph. An edge can be inserted across a face between two vertices on the face boundary (we call such a vertex pair linkable), and edges can be deleted. The…

Data Structures and Algorithms · Computer Science 2017-04-04 Jacob Holm , Eva Rotenberg

We study the problem of Upward Point-Set Embeddability, that is the problem of deciding whether a given upward planar digraph $D$ has an upward planar embedding into a point set $S$. We show that any switch tree admits an upward planar…

Data Structures and Algorithms · Computer Science 2015-05-20 Markus Geyer , Michael Kaufmann , Tamara Mchedlidze , Antonios Symvonis

We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and…

Data Structures and Algorithms · Computer Science 2017-08-31 Michael A. Bekos , Henry Förster , Michael Kaufmann

We study monotone simultaneous embeddings of upward planar digraphs, which are simultaneous embeddings where the drawing of each digraph is upward planar, and the directions of the upwardness of different graphs can differ. We first…

Computational Geometry · Computer Science 2014-03-03 Oswin Aichholzer , Thomas Hackl , Sarah Lutteropp , Tamara Mchedlidze , Alexander Pilz , Birgit Vogtenhuber

We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many connections…

Computational Geometry · Computer Science 2016-09-02 Steven Chaplick , Krzysztof Fleszar , Fabian Lipp , Alexander Ravsky , Oleg Verbitsky , Alexander Wolff

We consider drawings of trees in which all edges incident to leaves can be extended to infinite rays without crossing, partitioning the plane into infinite convex polygons. Among all such drawings we seek the one maximizing the angular…

Computational Geometry · Computer Science 2007-05-23 Josiah Carlson , David Eppstein

We obtain new parameterized algorithms for the classical problem of determining whether a directed acyclic graph admits an upward planar drawing. Our results include a new fixed-parameter algorithm parameterized by the number of sources, an…

Computational Geometry · Computer Science 2022-03-11 Steven Chaplick , Emilio Di Giacomo , Fabrizio Frati , Robert Ganian , Chrysanthi N. Raftopoulou , Kirill Simonov

A planar orthogonal drawing of a planar 4-graph G (i.e., a planar graph with vertex-degree at most four) is a crossing-free drawing that maps each vertex of G to a distinct point of the plane and each edge of $G$ to a sequence of horizontal…

Computational Geometry · Computer Science 2022-05-17 Walter Didimo , Michael Kaufmann , Giuseppe Liotta , Giacomo Ortali

Any planar graph has a crossing-free straight-line drawing in the plane. A simultaneous geometric embedding of two n-vertex graphs is a straight-line drawing of both graphs on a common set of n points, such that the edges withing each…

Computational Geometry · Computer Science 2007-05-23 Martin Kutz
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