# Rectangular Drawings of Plane Graphs Without Designated Corners

- First Online:

DOI: 10.1007/3-540-44968-X_9

- 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## Preview

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