Journal of Graph Algorithms and Applications

Drawing Halin-graphs with small height

Therese Biedl and Milap Sheth

Vol. 26, no. 4, pp. 473-502, 2022. Regular paper.

Abstract In this paper, we study how to draw Halin-graphs, i.e., planar graphs that consist of a tree $T$ and a cycle among the leaves of that tree. Based on tree-drawing algorithms and the pathwidth $pw(T) $, a well-known graph parameter, we find poly-line drawings of height at most $6pw(T)+3\in O(\log n)$. We also give an algorithm for straight-line drawings, and achieve height at most $12pw(T)-1$ for Halin-graphs, and smaller if the Halin-graph is cubic. We show that the height achieved by our algorithms is optimal in the worst case (i.e. for some Halin-graphs).