Sphericity exceeds cubicity for almost all complete bipartite graphs

We will prove that sphericity exceeds cubicity for complete bipartite graphs K(m,n) with max (m,n) > n₀, that sph K(n,n) ≥ n, and that as a result of the latter there is a complete bipartite graph with sphericity exceeding cubicity for every value of cubicity at least 6. This answers the question of Fishburn [1].