Abstract
A radial drawing is a representation of a graph in which the vertices lie on concentric circles of finite radius. In this paper we study the problem of computing radial drawings of planar graphs by using the minimum number of concentric circles. We assume that the edges are drawn as straight-line segments and that co-circular vertices can be adjacent. It is proven that the problem can be solved in polynomial time.
Highlights
A radial drawing is a representation of a graph in which the vertices are constrained to lie on concentric circles of finite radius
Based on the characterization above, we show that there exists a polynomial time algorithm to compute a minimum radial drawing of a planar graph
Based on the result of Theorem 3, we can show that the problem of computing a minimum radial drawing of a planar graph G can be solved in polynomial time
Summary
A radial drawing is a representation of a graph in which the vertices are constrained to lie on concentric circles of finite radius. In this paper we assume that the partition of the vertices of G is not given and study the problem of computing a partition that minimizes the number of levels, i.e. that corresponds to a crossing-free straight-line radial drawing of G on the minimum number of circles. The drawing has the additional property of being “proper”, i.e. an edge always connects either co-circular vertices or vertices on consecutive circles This contrasts with a result by Heath and Rosenberg [16] who prove that it is NP-complete to decide whether a planar graph admits a proper crossing-free layered drawing with vertices on parallel straight lines and no intra-layer edges.
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