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.
This work was partially supported by MIUR (Italy), Projects AlgoDEEP number 2008TFBWL4 and FIRB “Advanced tracking system in intermodal freight transportation” number RBIP06BZW8, by the German Research Foundation (DFG), project KA 812/15-1 ’Graph Drawing for Business Processes’, and by the National Technical University of Athens research program ΠEBE 2008.
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Angelini, P., Frati, F., Geyer, M., Kaufmann, M., Mchedlidze, T., Symvonis, A.: Upward geometric graph embeddings into point sets. Tech. Report 177, Dipartimento di Informatica e Automazione, Università Roma Tre (2010)
Badent, M., Di Giacomo, E., Liotta, G.: Drawing colored graphs on colored points. Theor. Comput. Sci. 408(2-3), 129–142 (2008)
Binucci, C., Di Giacomo, E., Didimo, W., Estrella-Balderrama, A., Frati, F., Kobourov, S., Liotta, G.: Upward straight-line embeddings of directed graphs into point sets. Computat. Geom. Th. Appl. 43, 219–232 (2010)
Bose, P.: On embedding an outer-planar graph in a point set. Computat. Geom. Th. Appl. 23(3), 303–312 (2002)
Bose, P., McAllister, M., Snoeyink, J.: Optimal algorithms to embed trees in a point set. J. Graph Alg. Appl. 1(2), 1–15 (1997)
Cabello, S.: Planar embeddability of the vertices of a graph using a fixed point set is NP-hard. J. Graph Alg. Appl. 10(2), 353–366 (2006)
Di Giacomo, E., Didimo, W., Liotta, G., Meijer, H., Trotta, F., Wismath, S.K.: k-colored point-set embeddability of outerplanar graphs. J. Graph Alg. Appl. 12(1), 29–49 (2008)
Giordano, F., Liotta, G., Mchedlidze, T., Symvonis, A.: Computing upward topological book embeddings of upward planar digraphs. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 172–183. Springer, Heidelberg (2007)
Gritzmann, P., Pach, B.M.J., Pollack, R.: Embedding a planar triangulation with vertices at specified positions. Amer. Math. Mont. 98, 165–166 (1991)
Kaufmann, M., Wiese, R.: Embedding vertices at points: Few bends suffice for planar graphs. J. Graph Alg. Appl. 6(1), 115–129 (2002)
Wiegers, M.: Recognizing outerplanar graphs in linear time. In: Tinhofer, G., Schmidt, G. (eds.) WG 1986. LNCS, vol. 246, pp. 165–176. Springer, Heidelberg (1987)
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Angelini, P., Frati, F., Geyer, M., Kaufmann, M., Mchedlidze, T., Symvonis, A. (2011). Upward Geometric Graph Embeddings into Point Sets. In: Brandes, U., Cornelsen, S. (eds) Graph Drawing. GD 2010. Lecture Notes in Computer Science, vol 6502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18469-7_3
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DOI: https://doi.org/10.1007/978-3-642-18469-7_3
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