Rectangular Drawings of Plane Graphs Without Designated Corners

Extended Abstract
  • Md. Saidur Rahman
  • Shin-ichi Nakano
  • Takao Nishizeki
Conference paper

DOI: 10.1007/3-540-44968-X_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1858)
Cite this paper as:
Rahman M.S., Nakano S., Nishizeki T. (2000) Rectangular Drawings of Plane Graphs Without Designated Corners. In: Du DZ., Eades P., Estivill-Castro V., Lin X., Sharma A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg

Abstract

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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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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