Khovanov complexes for bipartite links

Recently, for a limited class of bipartite links, the complicated Khovanov–Rozansky matrix factorization technique was reduced to an analogue of elementary Kauffman–Khovanov cycle calculus for an arbitrary N. In this note, we demonstrate the consistency of such reduction with the computation of bipartite Khovanov polynomials for N=2. Namely, we explain how Kauffman–Khovanov 22-hypercube is shrinked to a bipartite 3-hypercube.