Upward geometric graph embeddings into point sets

Authors:
Patrizio Angelini;Fabrizio Frati;Markus Geyer;Michael Kaufmann;Tamara Mchedlidze;Antonios Symvonis
Affiliations:
Dipartimento di Informatica e Automazione, Università Roma Tre, Italy;Dipartimento di Informatica e Automazione, Università Roma Tre, Italy;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany;Dept. of Mathematics, National Technical University of Athens, Athens, Greece;Dept. of Mathematics, National Technical University of Athens, Athens, Greece
Venue:
GD'10 Proceedings of the 18th international conference on Graph drawing
Year:
2010

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Abstract

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.