Testing Cyclic Level and Simultaneous Level Planarity

In this paper we prove that testing the cyclic level planarity of a cyclic level graph is a polynomial-time solvable problem. This is achieved by introducing and studying a generalization of this problem, which we call cyclic T -level planarity. Moreover, we show a complexity dichotomy for testing the simultaneous level planarity of a set of level graphs, with respect to both the number of level graphs and the number of levels.