- UPRIGHT DRAWINGS OF GRAPHS ON THREE LAYERS
- Alam, Muhammad Jawaherul ; Rabbi, Md. Mashfiqui ; Rahman, Md. Saidur ; Karim, Md. Rezaul ;
- Journal of applied mathematics & informatics, volume 28, issue 5_6, 2010, Pages 1347~1358
Abstract
An upright drawing of a planar graph G on k layers is a planar straight-line drawing of G, where the vertices of G are placed on a set of k horizontal lines, called layers and no two adjacent vertices are placed on the same layer. There is a previously known algorithm that decides in linear time whether a planar graph admits an upright drawing on k layers for a fixed value of k. However, the constant factor in the running time of the algorithm increases exponentially with k and makes it impractical even for k = 3. In this paper, we give a linear-time algorithm to examine whether a biconnected planar graph G admits an upright drawing on three layers and to obtain such a drawing if it exists. We also give a necessary and sufficient condition for a tree to have an upright drawing on three layers. Our algorithms in both the cases are much simpler and easier to implement than the previously known algorithms.