Abstract

A level graph G = (V; E; OE) is a directed acyclic graph with a mapping OE : V ! f1; 2; : : : ; kg, k 1, that partitions the vertex set V as V = V 1 [V 2 [ \Delta \Delta \Delta [V k , V j = OE \Gamma1 (j), V i " V j = ; for i 6= j, such that OE(v) OE(u) + 1 for each edge (u; v) 2 E. The level planarity testing problem is to decide if G can be drawn in the plane such that for each level V i , all v 2 V i are drawn on the line l i = f(x; k \Gamma i) j x 2 Rg, the edges are drawn monotone with respect to the vertical direction, and no edges intersect except at their end vertices. If G has a single source, the test can be performed in O(jV j) time by an algorithm of Di Battista and Nardelli [1988] that uses the PQ-tree data structure introduced by Booth and Lueker [1976]. PQ-trees have also been proposed by Heath and Pemmaraju [1995, 1996] to test level planarity of level directed acyclic graphs with several sources and sinks. It has been shown in Jünger, Leipert, and...

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