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≥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.
@article{arxiv.2401.03226,
title = {On 1-bend Upward Point-set Embeddings of $st$-digraphs},
author = {Emilio Di Giacomo and Henry Förster and Daria Kokhovich and Tamara Mchedlidze and Fabrizio Montecchiani and Antonios Symvonis and Anaïs Villedieu},
journal= {arXiv preprint arXiv:2401.03226},
year = {2024}
}