1 research outputs found
On the edge-length ratio of 2-trees
We study planar straight-line drawings of graphs that minimize the ratio
between the length of the longest and the shortest edge. We answer a question
of Lazard et al. [Theor. Comput. Sci. 770 (2019), 88--94] and, for any given
constant , we provide a -tree which does not admit a planar straight-line
drawing with a ratio bounded by . When the ratio is restricted to adjacent
edges only, we prove that any -tree admits a planar straight-line drawing
whose edge-length ratio is at most for any arbitrarily small
, hence the upper bound on the local edge-length ratio of
partial -trees is .Comment: Appears in the Proceedings of the 28th International Symposium on
Graph Drawing and Network Visualization (GD 2020