Skip to main content

Geometric Graphs in the Plane Lattice

  • Chapter

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7579))

Abstract

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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)

    Google Scholar 

  2. Kano, M., Suzuki, K.: Discrete geometry on red and blue points in the plane lattice (preprint)

    Google Scholar 

  3. Battista, G.D., Eardes, P., Tamassia, R., Tollis, I.G.: Graph drawing. Printice-Hall (1999)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  5. Nishizeki, T., Rahman, M.S.: Planar graph drawing. World Scientific (2004)

    Google Scholar 

  6. Pach, J. (ed.): Towards a theory of geometric graphs. Contemporary Mathematics, vol. 342. AMS (2004)

    Google Scholar 

  7. Raghavan, R., Cohoon, J., Sahni, S.: Single bend wiring. J. of Algorithms 7, 232–257 (1986)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kano, M., Suzuki, K. (2012). Geometric Graphs in the Plane Lattice. In: Márquez, A., Ramos, P., Urrutia, J. (eds) Computational Geometry. EGC 2011. Lecture Notes in Computer Science, vol 7579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34191-5_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34191-5_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34190-8

  • Online ISBN: 978-3-642-34191-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics