On 1-bend Upward Point-set Embeddings of $st$-digraphs

Emilio Di Giacomo; Henry Förster; Daria Kokhovich; Tamara Mchedlidze; Fabrizio Montecchiani; Antonios Symvonis; Anaïs Villedieu

arXiv · 2401.03226

On 1-bend Upward Point-set Embeddings of $st$-digraphs

Emilio Di Giacomo·Henry Förster·Daria Kokhovich·Tamara Mchedlidze·Fabrizio Montecchiani·Antonios Symvonis·Anaïs Villedieu

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Abstract

We study the upward point-set embeddability of digraphs on one-sided convex point sets with at most 1 bend per edge. We provide an algorithm to compute a 1-bend upward point-set embedding of outerplanar $st$-digraphs on arbitrary one-sided convex point sets. We complement this result by proving that for every $n \geq 18$ there exists a $2$-outerplanar $st$-digraph $G$ with $n$ vertices and a one-sided convex point set $S$ so that $G$ does not admit a 1-bend upward point-set embedding on $S$.

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Emilio Di Giacomo, Henry Förster, Daria Kokhovich, Tamara Mchedlidze, Fabrizio Montecchiani, Antonios Symvonis, Anaïs Villedieu. 2024-01-06. On 1-bend Upward Point-set Embeddings of $st$-digraphs. https://arxiv.org/abs/2401.03226

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