# Rectangular Drawings of Plane Graphs Without Designated Corners

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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## Preview

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