Drawing Halin-graphs with small height

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 ∈ 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).