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Rectangular Drawings of Plane Graphs Without Designated Corners

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Computing and Combinatorics (COCOON 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1858))

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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.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka, 100, Bangladesh

    Md. Saidur Rahman

  2. Department of Computer Science, Gunma University, Kiryu, 376-8515, Japan

    Shin-ichi Nakano

  3. Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai, 980-8579, Japan

    Takao Nishizeki

Authors
  1. Md. Saidur Rahman
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  2. Shin-ichi Nakano
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  3. Takao Nishizeki
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, MN 55455, Minneapolis, USA

    Ding-Zhu Du

  2. Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia

    Peter Eades  & Vladimir Estivill-Castro  & 

  3. School of Computer Science and Engineering, University of Newcastle, NSW 2052, Sydney, Australia

    Xuemin Lin  & Arun Sharma  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Rahman, M.S., Nakano, Si., 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. https://doi.org/10.1007/3-540-44968-X_9

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  • DOI: https://doi.org/10.1007/3-540-44968-X_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67787-1

  • Online ISBN: 978-3-540-44968-3

  • eBook Packages: Springer Book Archive

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