DeepAI AI Chat
Log In Sign Up

Segment representations with small resolution

10/16/2018
by   Therese Biedl, et al.
0

A segment representation of a graph is an assignment of line segments in 2D to the vertices in such a way that two segments intersect if and only if the corresponding vertices are adjacent. Not all graphs have such segment representations, but they exist, for example, for all planar graphs. In this note, we study the resolution that can be achieved for segment representations, presuming the ends of segments must be on integer grid points. We show that any planar graph (and more generally, any graph that has a so-called L-representation) has a segment representation in a grid of width and height 4^n.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/20/2019

Drawing planar graphs with few segments on a polynomial grid

The visual complexity of a plane graph drawing is defined to be the numb...
01/18/2018

Graph Based Analysis for Gene Segment Organization In a Scrambled Genome

DNA rearrangement processes recombine gene segments that are organized o...
02/21/2022

Geometry-Aware Planar Embedding of Treelike Structures

The growing complexity of spatial and structural information in 3D data ...
07/08/2020

A characterization of 2-threshold functions via pairs of prime segments

A {0,1}-valued function on a two-dimensional rectangular grid is called ...
09/09/2020

Deterministic Linear Time Constrained Triangulation using Simplified Earcut

Triangulation algorithms that conform to a set of non-intersecting input...
04/04/2022

Stacked Tensegrity Mechanism for Medical Application

In this article a multi-segmented planar tensegrity mechanism was presen...
10/12/2017

4-connected planar graphs are in B_3-EPG

We show that every 4-connected planar graph has a B_3-EPG representation...