Chord Diagrams and Gauss Codes for Graphs

Authors

Thomas Fleming
Blake Mellor, Loyola Marymount UniversityFollow

Document Type

Article - post-print

Publication Date

2006

Abstract

Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study of spatial graphs. We will define chord diagrams for planar embeddings of planar graphs and their intersection graphs, and prove some basic results. Then, as an application, we will introduce Gauss codes for immersions of graphs in the plane and give algorithms to determine whether a particular crossing sequence is realizable as the Gauss code of an immersed graph.

Comments

This is a post-print version of the article.

Original Publication Citation

Fleming, T. and B. Mellor, 2006: Chord Diagrams and Gauss Codes for Graphs. arXiv:math.CO/0508269.

Digital Commons @ LMU & LLS Citation

Fleming, Thomas and Mellor, Blake, "Chord Diagrams and Gauss Codes for Graphs" (2006). Mathematics, Statistics and Data Science Faculty Works. 18.
https://digitalcommons.lmu.edu/math_fac/18