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We present two graph drawing algorithms based on the recently defined "grand-Schnyder woods", which are a far-reaching generalization of the classical Schnyder woods. The first is a straight-line drawing algorithm for plane graphs with…

Combinatorics · Mathematics 2025-03-04 Olivier Bernardi , Éric Fusy , Shizhe Liang

A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…

Computational Geometry · Computer Science 2025-02-06 Walter Didimo , Giuseppe Liotta , Giacomo Ortali , Maurizio Patrignani

Topological drawings are representations of graphs in the plane, where vertices are represented by points, and edges by simple curves connecting the points. A drawing is simple if two edges intersect at most in a single point, either at a…

Computational Geometry · Computer Science 2022-09-08 Alfredo García , Alexander Pilz , Javier Tejel

A natural way to represent on the plane both a planar graph and its dual is to follow the definition of the dual, thus, to place vertices inside their corresponding primal faces, and to draw the dual edges so that they only cross their…

Computational Geometry · Computer Science 2015-05-12 Tamara Mchedlidze

Canonical orderings serve as the basis for many incremental planar drawing algorithms. All these techniques, however, have in common that they are limited to undirected graphs. While $st$-orderings do extend to directed graphs, especially…

Data Structures and Algorithms · Computer Science 2016-08-31 Martin Gronemann

We study the problem of embedding graphs in the plane as good geometric spanners. That is, for a graph $G$, the goal is to construct a straight-line drawing $\Gamma$ of $G$ in the plane such that, for any two vertices $u$ and $v$ of $G$,…

Data Structures and Algorithms · Computer Science 2020-02-14 Oswin Aichholzer , Manuel Borrazzo , Prosenjit Bose , Jean Cardinal , Fabrizio Frati , Pat Morin , Birgit Vogtenhuber

In the Partially Embedded Planarity problem, we are given a graph $G$ together with a topological drawing of a subgraph $H$ of $G$. The task is to decide whether the drawing can be extended to a drawing of the whole graph such that no two…

Computational Geometry · Computer Science 2024-10-18 Simon D. Fink , Ignaz Rutter , Sandhya T. P

Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…

Populations and Evolution · Quantitative Biology 2013-10-09 Piotr Plonski , Jan P. Radomski

A graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. However, there are 1-planar graphs which do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line…

Computational Geometry · Computer Science 2021-09-07 Franz J. Brandenburg

We show how to test in linear time whether an outerplanar graph admits a planar rectilinear drawing, both if the graph has a prescribed plane embedding that the drawing has to respect and if it does not. Our algorithm returns a planar…

Data Structures and Algorithms · Computer Science 2020-08-24 Fabrizio Frati

We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…

Data Structures and Algorithms · Computer Science 2022-09-29 Jacob Holm , Ivor van der Hoog , Eva Rotenberg

We consider graph drawing algorithms for learning spaces, a type of st-oriented partial cube derived from antimatroids and used to model states of knowledge of students. We show how to draw any st-planar learning space so all internal faces…

Computational Geometry · Computer Science 2008-06-30 David Eppstein

Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as…

Computational Geometry · Computer Science 2014-01-22 Mohamed A. El-Sayed , S. Abdel-Khalek , Hanan H. Amin

We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…

Discrete Mathematics · Computer Science 2017-03-23 Glencora Borradaile , Jeff Erickson , Hung Le , Robbie Weber

In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…

Computational Geometry · Computer Science 2007-05-23 Matthew Dickerson , David Eppstein , Michael T. Goodrich , Jeremy Meng

In this paper, we study planar drawings of maximal outerplanar graphs with the objective of achieving small height. A recent paper gave an algorithm for such drawings that is within a factor of 4 of the optimum height. In this paper, we…

Data Structures and Algorithms · Computer Science 2017-02-07 Therese Biedl , Philippe Demontigny

We show that the 1-planar slope number of 3-connected cubic 1-planar graphs is at most 4 when edges are drawn as polygonal curves with at most 1 bend each. This bound is obtained by drawings whose vertex and crossing resolution is at least…

Computational Geometry · Computer Science 2018-08-28 Philipp Kindermann , Fabrizio Montecchiani , Lena Schlipf , André Schulz

We investigate the problem of drawing two posets of the same ground set so that one is drawn from left to right and the other one is drawn from the bottom up. The input to this problem is a directed graph $G = (V, E)$ and two sets $X, Y$…

Computational Geometry · Computer Science 2020-10-27 Guido Brückner , Vera Chekan

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…

Computational Geometry · Computer Science 2016-07-19 Franz J. Brandenburg , Walter Didimo , William S. Evans , Philipp Kindermann , Giuseppe Liotta , Fabrizio Montecchiani

Tanglegrams are formed by taking two rooted binary trees $T$ and $S$ with the same number of leaves and uniquely matching each leaf in $T$ with a leaf in $S$. They are usually represented using layouts, which embed the trees and the…

Combinatorics · Mathematics 2022-06-14 Kevin Liu