# Radial Level Planarity Testing and Embedding in Linear Time

### Abstract

Every planar graph has a concentric representation based on a breadth first search, see [21]. The vertices are placed on concentric circles and the edges are routed as curves without crossings. Here we take the opposite view. A graph with a given partitioning of its vertices onto k concentric circles is k-radial planar, if the edges can be routed monotonic between the circles without crossings. Radial planarity is a generalisation of level planarity, where the vertices are placed on k horizontal lines. We extend the technique for level planarity testing of [12,13,15–18] and show that radial planarity is decidable in linear time, and that a radial planar embedding can be computed in linear time.

Publication
Giuseppe Liotta (ed.), Proc. Graph Drawing, GD 2003, Lecture Notes in Computer Science 2919:393–405 Springer