In a previous paper [J. Comb. Theory, Ser. A 89, 77-104 (2000; Zbl 0959.52010)] the authors characterized the cone of linear inequalities holding for the flag \(f\)-vectors of all graded posets of a given rank. In the paper under review they give a description of the cone of flag \(f\)-vectors of planar graded posets. The proof includes a special chain-edge FA-labeling which generalizes the notion of lexicographic shelling, or CL-labeling. The use of FA-labeling yields a simple enumeration of the facets in the order complex of an arbitrary graded poset such that the intersection of each facet with the previously attached facets is homotopic to a ball or to a sphere.