# Minimum-width grid drawings of plane graphs extend abstract

## Abstract

Given a plane graph *G*, we wish to draw it in the plane, according to the given embedding, in such a way that the vertices of *G* are drawn as grid points, and the edges are drawn as straight-line segments between their endpoints. An additional objective is to minimize the size of the resulting grid. It is known that each plane graph can be drawn in such a way in a (*n*−2)×(*n*−2) grid (for *n*≥3), and that no grid smaller than (2*n*/3−1)×(2*n*/3−1) can be used for this purpose, if *n* is a multiple of 3. In fact, it can be shown that, for all *n*≥3, each dimension of the resulting grid needs to be at least [2(*n*−1)/3], even if the other one is allowed to be infinite. In this paper we show that this bound is tight, by presenting a grid drawing algorithm that produces drawings of width [2(*n*−1)/3]. The height of the produced drawings is bounded by 4[2(*n*−1)/3]−1.

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