On multipartite posets (Q2519843)

A poset \(P=(X,\leq )\) is called \(m\)-bipartite (\(m\geq 2\)) if \(X\) is a partition \(X=X_1\cup \dots\cup X_m\) such that \(X_i\) is an antichain in \(P\) and \(x<y\) implies \(x\in X_i\) and \(y\in X_j\), where \(i<j\). This notion is a generalization of that of a bipartite poset. The author derives a tight asymptotic upper bound on the order dimension of \(m\)-partite posets.