Bipartite complements of circle graphs

TL;DR

This paper provides an elementary proof that bipartite graphs which are complements of circle graphs are themselves circle graphs, simplifying Bouchet's original algebraic proof from 1999.

Contribution

The paper offers a new, elementary proof of Bouchet's 1999 result regarding bipartite complements of circle graphs.

Findings

Bipartite complements of circle graphs are themselves circle graphs

Elementary proof replaces algebraic methods used previously

Simplifies understanding of the structure of circle graphs

Abstract

Using an algebraic characterization of circle graphs, Bouchet proved in 1999 that if a bipartite graph $G$ is the complement of a circle graph, then $G$ is a circle graph. We give an elementary proof of this result.