Przytycki–Silvero conjecture on independence complexes of circle graphs

A circle graph is the intersection graph of a chord diagram, and for a simple graph $G$, its independence complex $I(G)$ is the simplicial complex whose simplices are the pairwise non-adjacent vertex subsets of $G$.

Przytycki–Silvero conjecture. If $G$ is a circle graph, then $I(G)$ has the homotopy type of a wedge of spheres.

The conjecture is motivated in part by the relationship between independence complexes of circle graphs and extreme Khovanov homology. Existing results support the conjecture, but the techniques cited in the source do not prove it in full generality.