TY - JOUR
AU - Biedl, Therese
AU - Sheth, Milap
PY - 2022/07/01
Y2 - 2024/06/13
TI - Drawing Halin-graphs with small height
JF - Journal of Graph Algorithms and Applications
JA - JGAA
VL - 26
IS - 4
SE -
DO - 10.7155/jgaa.00604
UR - https://jgaa.info/index.php/jgaa/article/view/paper604
SP - 473-502
AB - In this paper, we study how to draw Halin-graphs, i.e., planar graphsthat 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, andachieve height at most $12pw(T)-1$ for Halin-graphs, andsmaller 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).
ER -