×

zbMATH — the first resource for mathematics

Geometric graphs in the plane lattice. (English) Zbl 1374.68353
Márquez, Alberto (ed.) et al., Computational geometry. XIV Spanish meeting on computational geometry, EGC 2011, dedicated to Ferran Hurtado on the occasion of his 60th birthday, Alcalá de Henares, Spain, June 27–30, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-34190-8/pbk). Lecture Notes in Computer Science 7579, 274-281 (2012).
Summary: An \(L\)-line segment in the plane consists of a vertical line segment and a horizontal line segment having a common end-point. In this paper, we consider some problems on non-crossing geometric embeddings of graphs in the plane lattice, whose vertices are given points of the plane lattice in general position and whose edges are suitable \(L\)-line segments.
For the entire collection see [Zbl 1253.68016].
Reviewer: Reviewer (Berlin)

MSC:
68R10 Graph theory (including graph drawing) in computer science
05C62 Graph representations (geometric and intersection representations, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kaneko, A., Kano, M.: Discrete geometry on red and blue points in the plane – A survey. In: Discrete and Computational Geometry. Algorithms and Combinatorics, vol. 25, pp. 551–570. Springer (2003) · Zbl 1079.52505
[2] Kano, M., Suzuki, K.: Discrete geometry on red and blue points in the plane lattice (preprint) · Zbl 1276.52014
[3] Battista, G.D., Eardes, P., Tamassia, R., Tollis, I.G.: Graph drawing. Printice-Hall (1999)
[4] Katz, B., Krug, M., Rutter, I., Wolff, A.: Manhattan-Geodesic Embedding of Planar Graphs. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 207–218. Springer, Heidelberg (2010) · Zbl 1284.68466 · doi:10.1007/978-3-642-11805-0_21
[5] Nishizeki, T., Rahman, M.S.: Planar graph drawing. World Scientific (2004) · Zbl 1070.68124 · doi:10.1142/5648
[6] Pach, J. (ed.): Towards a theory of geometric graphs. Contemporary Mathematics, vol. 342. AMS (2004) · Zbl 1052.05004
[7] Raghavan, R., Cohoon, J., Sahni, S.: Single bend wiring. J. of Algorithms 7, 232–257 (1986) · Zbl 0606.94019 · doi:10.1016/0196-6774(86)90006-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.