# Grid embedding of 4-connected plane graphs

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## Abstract

A straight line grid embedding of a plane graph *G* is a drawing of *G* such that the vertices are drawn at grid points and the edges are drawn as non-intersecting straight line segments. In this paper, we show that, if a 4-connected plane graph *G* has at least 4 vertices on its exterior face, then *G* can be embedded on a grid of size W×H such that *W+H≤n, W≤(n*+3)/2 and *H≤2(n*−1)/3, where *n* is the number of vertices of *G*. Such an embedding can be computed in linear time.

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