Universal Line-Sets for Drawing Planar 3-Trees [chapter]

Md. Iqbal Hossain, Debajyoti Mondal, Md. Saidur Rahman, Sammi Abida Salma
2012 Lecture Notes in Computer Science  
A set S of lines is universal for drawing planar graphs with n vertices if every planar graph G with n vertices can be drawn on S such that each vertex of G is drawn as a point on a line of S and each edge is drawn as a straight-line segment without any edge crossing. It is known that 2(n−1) 3 parallel lines are universal for any planar graph with n vertices. In this paper we show that a set of n−3 2 + 3 parallel lines or a set of n+3 4 concentric circles are universal for drawing planar
more » ... with n vertices. In both cases we give linear-time algorithms to find such drawings. A by-product of our algorithm is the generalization of the known bijection between plane 3-trees and rooted full ternary trees to the bijection between planar 3-trees and unrooted full ternary trees. We also identify some subclasses of planar 3-trees whose drawings are supported by fewer than n−3 2 + 3 parallel lines.
doi:10.1007/978-3-642-28076-4_15 fatcat:oeaxafsnqbfnhlphusp5pijtlm