We study the problem of characterizing the directed graphs with an upward straight-line embedding into every point set in general or in convex position. We solve two questions posed by Binucci et al. [Computational Geometry: Theory and Applications, 2010]. Namely, we prove that the classes of directed graphs with an upward straight-line embedding into every point set in convex position and with an upward straight-line embedding into every point set in general position do not coincide, and we prove that every directed caterpillar admits an upward straight-line embedding into every point set in convex position. Further, we provide new partial positive results on the problem of constructing upward straight-line embeddings of directed paths into point sets in general position. © 2011 Springer-Verlag.
CITATION STYLE
Angelini, P., Frati, F., Geyer, M., Kaufmann, M., Mchedlidze, T., & Symvonis, A. (2011). Upward geometric graph embeddings into point sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6502 LNCS, pp. 25–37). https://doi.org/10.1007/978-3-642-18469-7_3
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