Characterization of Unlabeled Radial Level Planar Graphs

Suppose that an n-vertex graph has a distinct labeling with the integers {1, . . . , n}. Such a graph is radial level planar if it admits a crossings-free drawing under two constraints. First, each vertex lies on a concentric circle such that the radius of the circle equals the label of the vertex. Second, each edge is drawn with a radially monotone curve. We characterize the set of unlabeled radial level planar (URLP) graphs that are radial level planar in terms of 7 and 15 forbidden subdivisions depending on whether the graph is disconnected or connected, respectively. We also provide linear-time drawing algorithms for any URLP graph