Chapter

Computing and Combinatorics

Volume 1858 of the series Lecture Notes in Computer Science pp 85-94

Date:

Rectangular Drawings of Plane Graphs Without Designated Corners

Extended Abstract
  • Md. Saidur RahmanAffiliated withDepartment of Computer Science and Engineering, Bangladesh University of Engineering and Technology
  • , Shin-ichi NakanoAffiliated withDepartment of Computer Science, Gunma University
  • , Takao NishizekiAffiliated withGraduate School of Information Sciences, Tohoku University

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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.

Key words

Graph Algorithm Graph Drawing Rectangular Drawing