Rectangular Drawings of Plane Graphs Without Designated Corners

Extended Abstract
  • Md. Saidur Rahman
  • Shin-ichi Nakano
  • Takao Nishizeki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1858)


A rectangular drawing of a plane graph G is a drawing of G such that each vertex is drawn as a point, each edge is drawn as a horizontal or a vertical line segment, and the contour of each face is drawn as a rectangle. A necessary and sufficient condition for the existence of a rectangular drawing has been known only for the case where exactly four vertices of degree 2 are designated as corners in a given plane graph G. In this paper we establish a necessary and sufficient condition for the existence of a rectangular drawing of G for the general case in which no vertices are designated as corners. We also give a linear-time algorithm to find a rectangular drawing of G if it exists.

Key words

Graph Algorithm Graph Drawing Rectangular Drawing 


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  1. [BS88]
    J. Bhasker and S. Sahni, A linear algorithm to find a rectangular dual of a planar triangulated graph, Algorithmica, 3 (1988), pp. 247–278.MATHCrossRefMathSciNetGoogle Scholar
  2. [DETT99]
    G. Di Battista, P. Eades, R. Tamassia and I. G. Tollis, Graph Drawing, Prentice Hall, Upper Saddle River, NJ, 1999.MATHCrossRefGoogle Scholar
  3. [H93]
    X. He, On finding the rectangular duals of planar triangulated graphs, SIAM J. Comput., 22(6) (1993), pp. 1218–1226.MATHCrossRefMathSciNetGoogle Scholar
  4. [H95]
    X. He, An efficient parallel algorithm for finding rectangular duals of plane triangulated graphs, Algorithmica 13 (1995), pp. 553–572.MATHCrossRefMathSciNetGoogle Scholar
  5. [KH97]
    G. Kant and X. He, Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems, Theoretical Computer Science, 172 (1997), pp. 175–193.MATHCrossRefMathSciNetGoogle Scholar
  6. [KK84]
    K. Kozminski and E. Kinnen, An algorithm for finding a rectangular dual of a planar graph for use in area planning for VLSI integrated circuits, Proc. 21st DAC, Albuquerque, June (1984), pp. 655–656.Google Scholar
  7. [L90]
    T. Lengauer, Combinatirial Algorithms for Integrated Circuit Layout, John Wiley & Sons, Chichester, 1990.Google Scholar
  8. [RNN98]
    M. S. Rahman, S. Nakano and T. Nishizeki, Rectangular grid drawings of plane graphs, Comp. Geom. Theo. Appl., 10(3) (1998), pp. 203–220.MATHMathSciNetGoogle Scholar
  9. [T84]
    C. Thomassen, Plane representations of graphs, Eds. J. A. Bondy and U. S. R. Murty, Progress in Graph Theory, Academic Press Canada, (1984), pp. 43–69.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Md. Saidur Rahman
    • 1
  • Shin-ichi Nakano
    • 2
  • Takao Nishizeki
    • 3
  1. 1.Department of Computer Science and EngineeringBangladesh University of Engineering and TechnologyDhakaBangladesh
  2. 2.Department of Computer ScienceGunma UniversityKiryuJapan
  3. 3.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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