The wedge-of-spheres conjecture for independence complexes of bipartite circle graphs

Let GG be a bipartite circle graph, namely a circle graph that is bipartite, and let I(G)I(G) be its independence complex, whose simplices are the subsets of pairwise non-adjacent vertices of GG. Bipartite wedge-of-spheres conjecture. The independence complex associated to a bipartite circle graph is homotopy equivalent to a wedge of spheres. This is the restriction relevant to Lando graphs, since the family of Lando graphs coincides with the family of bipartite circle graphs. If true, the conjecture would imply that the extreme Khovanov homology of any diagram is torsion-free and provide an obstruction to a link being Khovanov AA-adequate. Its status is not resolved in the supplied source.

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Primary source

Lizzie Buchanan, Huizheng Guo, Gabriel Montoya-Vega, Yongwu Rong and Marithania Silvero, “On the notion of Khovanov A-adequacy”, arXiv:2502.17637 (2025).

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