A bipartite planar graph with n vertices has at most 2n edges. As a generalization of this well-known result, Kalai, Nevo and Novik conjectured that for a simplicial complex that is PL-embeddable in Euclidean 2k-space and has a (k+1)-colorable 1-skeleton, the number of k-dimensional faces is at most twice the number of (k-1)-dimensional faces. In my talk, I will present a proof of this conjecture based on the multigraded strong Lefschetz property of the face ring.