Chord Diagrams and Gauss Codes for Graphs

Details Chord Diagrams and Gauss Codes for Graphs Chord Diagrams and Gauss Codes for Graphs

2005-08-15

arxiv.org/abs/math/0508269v2

Mathematics

Combinatorics

20 pages, many figures. This version has been substantially rewritten, and the results are stronger

Scientific paper

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.

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