On the Complexity of Clustered-Level Planarity and T-Level Planarity
  In this paper we study two problems related to the drawing of level graphs, that is, T-LEVEL PLANARITY and CLUSTERED-LEVEL PLANARITY. We show that both problems are NP-complete in the general case and that they become polynomial-time solvable when restricted to proper instances. 
Patrizio Angelini and Giordano Da Lozzo and Giuseppe Di Battista and   Fabrizio Frati and Vincenzo Roselli
cs.DS cs.CG