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arXiv · 1909.11152

On the edge-length ratio of 2-trees

Václav Blažej·Jiří Fiala·Giuseppe Liotta
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Abstract

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 $r$, we provide a $2$-tree which does not admit a planar straight-line drawing with a ratio bounded by $r$. When the ratio is restricted to adjacent edges only, we prove that any $2$-tree admits a planar straight-line drawing whose edge-length ratio is at most $4 + \varepsilon$ for any arbitrarily small $\varepsilon > 0$, hence the upper bound on the local edge-length ratio of partial $2$-trees is $4$.

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Václav Blažej, Jiří Fiala, Giuseppe Liotta. 2019-09-24. On the edge-length ratio of 2-trees. https://arxiv.org/abs/1909.11152

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