Przytycki–Silvero conjecture for bipartite circle graphs

A circle graph is the intersection graph of a chord diagram, a graph is bipartite if its vertices can be partitioned into two independent sets, 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 for bipartite circle graphs. If $G$ is a bipartite circle graph, then $I(G)$ has the homotopy type of a wedge of spheres.

This is presented as a weaker version of the general Przytycki–Silvero conjecture and is especially relevant to Khovanov homology, since the graphs arising from link diagrams are bipartite. Its status is not resolved in the supplied text.