Results 11 to 20 of about 65,390 (252)

Drawing Planar Graphs with a Prescribed Inner Face [PDF]

, 2013
Given a plane graph $G$ (i.e., a planar graph with a fixed planar embedding) and a simple cycle $C$ in $G$ whose vertices are mapped to a convex polygon, we consider the question whether this drawing can be extended to a planar straight-line drawing of ...
C.A. Duncan, D. Avis, E.W. Chambers, J. Pach, M. Patrignani, S.-H. Hong, V. Jelínek, W.T. Tutte   +7 more
core   +2 more sources

Stabbing line segments with disks: complexity and approximation algorithms [PDF]

, 2017
Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii $r>0$ where the set of segments forms a straight line drawing $G=(V,E)$ of
Kobylkin, Konstantin
core   +1 more source

Strongly Monotone Drawings of Planar Graphs [PDF]

, 2016
A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the ...
Felsner, Stefan, Igamberdiev, Alexander, Kindermann, Philipp, Klemz, Boris, Mchedlidze, Tamara, Scheucher, Manfred   +5 more
core   +2 more sources

On Universal Point Sets for Planar Graphs [PDF]

, 2013
A set P of points in R^2 is n-universal, if every planar graph on n vertices admits a plane straight-line embedding on P. Answering a question by Kobourov, we show that there is no n-universal point set of size n, for any n>=15.
Cardinal, Jean, Hoffmann, Michael, Kusters, Vincent   +2 more
core   +2 more sources

Recognizing and Drawing IC-planar Graphs

, 2015
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.
C Auer, C Auer, C Binucci, C Thomassen, D Král, E Ackerman, E Giacomo Di, E Giacomo Di, E Giacomo Di, EN Argyriou, FJ Brandenburg, H Fraysseix de, J Fox, J Pach, M Chrobak, MA Bekos, MJ Alam, MR Garey, O Cheong, OV Borodin, P Eades, S Hong, S-H Hong, VP Korzhik, W Didimo, W Didimo, X Zhang, X Zhang   +27 more
core   +1 more source

Convex drawings of hierarchical planar graphs and clustered planar graphs [PDF]

, 1906
In this paper, we present results on convex drawings of hierarchical graphs and clustered graphs. A convex drawing is a planar straight-line drawing of a plane graph, where every facial cycle is drawn as a convex polygon.
Hong, Seok-Hee, Nagamochi, Hiroshi
core   +1 more source

Unbiased Finite Element Mesh Delaunay Constrained Triangulation Applied to 2D Images with High Morphological Complexity Using Mathematical Morphology Tools Part 2: Labeled Images

Computation
We propose a method for generating a constrained Delaunay triangulation CDT applied to labeled 2D images with high morphological complexity. In the previous paper, Part 1, we established an unbiased planar straight-line graph (PLSG) on image objects of ...
F. N’Guyen, T. Kanit, A. Imad
doaj   +1 more source

Obstacle Numbers of Planar Graphs

, 2017
Given finitely many connected polygonal obstacles $O_1,\dots,O_k$ in the plane and a set $P$ of points in general position and not in any obstacle, the {\em visibility graph} of $P$ with obstacles $O_1,\dots,O_k$ is the (geometric) graph with vertex set $
B Mohar, H Alpert, H Fraysseix de, H Fraysseix de, I Fáry, J Pach, M Balko, SK Ghosh, SK Ghosh, WT Tutte   +9 more
core   +1 more source

Drawing graphs with vertices and edges in convex position [PDF]

, 2015
A graph has strong convex dimension $2$, if it admits a straight-line drawing in the plane such that its vertices are in convex position and the midpoints of its edges are also in convex position.
Hans Raj Tiwary, N Halman, S Onn
core   +6 more sources

Unrolling of Syngonium podophyllum: Functional Anatomy, Morphology and Modelling of Its Peltate Leaves

Advanced Biology, EarlyView.
The unrolling of the peltate leaves in Syngonium podophyllum is analyzed and quantified (left‐hand side to center). These measurements serve to verify a mathematical model for leaf unrolling based on the model used in Schmidt (2007). An additional formula for obtaining a layer mismatch from a prescribed radius is derived.
Michelle Modert, Nick Seinsche, Sören Bartels, Tom Masselter, Thomas Speck   +4 more
wiley   +1 more source