Grid Drawings of FourConnected Plane GraphsMiura, Kazuyuki and Nakano, ShinIchi and Nishizeki, Takao (1999) Grid Drawings of FourConnected Plane Graphs. In: Graph Drawing 7th International Symposium, GD’99, September 1519, 1999 , pp. 145154(Official URL: http://dx.doi.org/10.1007/3540466487_15). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540466487_15
AbstractA grid drawing of a plane graph G is a drawing of G on the plane so that all vertices of G are put on plane grid points and all edges are drawn as straight line segments between their endpoints without any edgeintersection. In this paper we give a very simple algorithm to find a grid drawing of any given 4connected plane graph G with four or more vertices on the outer face. The algorithm takes time O(n) and needs a rectangular grid of width \lceil n/2 \rceil  1 and height \lceil n/2 \rceil if G has n vertices. The algorithm is best possible in the sense that there are an infinite number of 4connected plane graphs any grid drawings of which need rectangular grids of width \lceil n/2 \rceil  1 and height \lceil n/2 \rceil.
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