Lattices contained in planar orders are planar (Q1208077)

The following is the main result of the paper. Let \(P\) be a finite ordered set with planar covering graph and let \(\text{cov}(P)\) be its planar representation. Let \(L\) be a truncated lattice contained in \(P\). Then the covering graph of \(L\) has a representation \(\text{cov}(L)\) in which, whenever \(b\) covers \(a\) in \(L\), the edge joining \(a\) to \(b\) may be taken as a curve following some covering chain in \(P\) from \(a\) to \(b\). Moreover, this representation \(\text{cov}(L)\) is planar, too.