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Drawing Halin-graphs with small height
arXiv - CS - Computational Geometry Pub Date : 2020-03-31 , DOI: arxiv-2003.14413
Therese Biedl and Milap Sheth

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).

中文翻译:

绘制小高度的Halin图

在本文中,我们研究如何绘制Halin 图,即由一棵树$T$ 和该树的叶子之间的循环组成的平面图。基于树绘制算法和路径宽度$ pw(T) $,一个众所周知的图形参数,我们找到高度最多$6pw(T)+3\in O(\log n)$ 的折线图。我们还给出了直线绘图的算法,Halin-graphs 的高度最多为 $12pw(T)+1$,如果 Halin-graph 是三次,则更小。我们表明,在最坏的情况下(即对于某些 Halin 图),我们的算法实现的高度是最佳的。
更新日期:2020-04-01
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