Circle graphs (chord interlacement graphs) of Gauss diagrams: Descriptions of realizable Gauss diagrams, algorithms, enumeration

08/05/2021
by   Abdullah Khan, et al.
0

Chord diagrams, under the name of Gauss diagrams, are used in low-dimensional topology as an important tool for studying curves or knots. Those Gauss diagrams that correspond to curves or knots are called realizable. The theme of our paper is the fact that realizability of a Gauss diagram can be expressed via its circle graph. Accordingly, one can define and study realizable circle graphs (with realizability of a circle graph understood as realizability of any one of chord diagrams corresponding to the graph). Several studies contain theorems purporting to prove the fact. We check several of these descriptions experimentally and find counterexamples to the descriptions of realizable Gauss diagrams in some of these publications. We formulate new descriptions of realizable circle graphs and present an elegant algorithm for checking if a circle graph is realizable. We enumerate realizable circle graphs for small sizes and comment on these numbers. Then we concentrate on one type of curves, called meanders, and study the circle graphs of their Gauss diagrams.

READ FULL TEXT
research
03/03/2021

Experimental Mathematics Approach to Gauss Diagrams Realizability

A Gauss diagram (or, more generally, a chord diagram) consists of a circ...
research
04/26/2023

Structure Diagram Recognition in Financial Announcements

Accurately extracting structured data from structure diagrams in financi...
research
04/30/2021

Number and quality of diagrams in scholarly publications is associated with number of citations

Diagrams are often used in scholarly communication. We analyse a corpus ...
research
04/05/2021

Integrating 2D and 3D Digital Plant Information Towards Automatic Generation of Digital Twins

Ongoing standardization in Industry 4.0 supports tool vendor neutral rep...
research
12/05/2019

Classifying Diagrams and Their Parts using Graph Neural Networks: A Comparison of Crowd-Sourced and Expert Annotations

This article compares two multimodal resources that consist of diagrams ...
research
09/27/2022

DeepVenn – a web application for the creation of area-proportional Venn diagrams using the deep learning framework Tensorflow.js

Motivation: The Venn diagram is one of the most popular methods to visua...
research
09/29/2021

Pigment Adsorption Optimization in Various Low Cost Adsorbents

Abstract: The applications of adsorption are very important. The followi...

Please sign up or login with your details

Forgot password? Click here to reset