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- W1546737255 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 (2n/3−1)×(2n/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." @default.
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- W1546737255 date "1995-01-01" @default.
- W1546737255 modified "2023-09-27" @default.
- W1546737255 title "Minimum-width grid drawings of plane graphs extend abstract" @default.
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- W1546737255 doi "https://doi.org/10.1007/3-540-58950-3_361" @default.
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